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Gemma 2B on 8.EE.C.8

Common Core Standard 8.EE.C.8

This standard covers the following:

Analyze and solve pairs of simultaneous linear equations.

🔗 Problem

Problem: Let's find the values of variables q and s by solving the following system of equations: 1. (40 * s) - (91 * q) = 37 2. (30 * s) + (12 * q) = 121

Gemma 2B:

 Reasoning:

1. (40 * s) - (91 * q) = 37
2. (30 * s) + (12 * q) = 121

Multiply both sides of the first equation by 12:

1. (40 * s) - (91 * q) = 37
2. (30 * s) + (12 * q) = 121

Multiply both sides of the second equation by 91:

1. (40 * s) - (91 * q) = 37
2. (30 * s) + (12 * q) = 121

Multiply both sides of the first equation by 30:

1. (40 * s) - (91 * q) = 37
2. (30 * s) + (12 * q) = 121

Multiply both sides of the second equation by 40:

1. (40 * s) - (91 * q) = 37
2. (30 * s) + (12 * q) = 121

Multiply both sides of the first equation by 12:

1. (40 * s) - (91 * q) = 37
2. (30 * s) + (12 * q) = 121

Multiply both sides of the second equation by 91:

1. (40 * s) - (91 * q) = 37
2. (30 * s) + (12 * q) = 121

Multiply both sides of the first equation by 30:

1. (40 * s) - (91 * q) = 37
2. (30 * s) + (12 * q) = 121

Multiply both sides of the second equation by 40:

1. (40 * s) - (91 * q) = 37
2. (30 * s) + (12 * q) = 121

Multiply both sides of the first equation by 12:

1. (40 * s) - (91 * q) = 37
2. (30 * s) + (12 * q) = 121

Multiply both sides of the second equation by 91:

1. (40 * s) - (91 * q) = 37
2. (30 * s) + (12 * q) = 121

Multiply both sides of the first equation by 30:

1. (40 * s) - (91 * q) = 37
2. (30 * s) + (12 * q) = 121

Multiply both sides of the second equation by 40:

1. (40 * s) - (91 * q) = 37
2. (30 * s) + (12 * q) = 121

Multiply both sides of the first equation by 12:

1. (40 * s) - (91 * q) = 37
2. (30 * s) + (12 * q) = 121

Multiply both sides of the second equation by 91:

1. (40 * s) - (91 * q) = 37
2. (30 * s) + (12 * q) = 121

Multiply both sides of the first equation by 30:

1. (40 * s) - (91 * q) = 37
2. (30 * s) + (12 * q) = 121

Multiply both sides of the second equation by 40:

1. (40 * s) - (91 * q) = 37
2. (30 * s) + (12 * q) = 121

Multiply both sides of the first equation by 12:

1. (40 * s)

Expected answer: {q: 373/321, s: 2291/642}

Correct? No

🔗 Problem

Problem: Solve the following system of equations for the values of b and m: 4 * b + 44 * m = 180 and 79 * m - 6 * b = 48.

Gemma 2B:

 Reasoning: 4 * b + 44 * m = 180
4 * b + 44 * m = 180
4 * b = 180 - 44 * m
b = (180 - 44 * m)/4
79 * m - 6 * b = 48
79 * m - 6 * (180 - 44 * m)/4 = 48
79 * m - 6 * (180 - 44 * m)/4 = 48
79 * m - 6 * (180 - 44 * m)/4 = 48
79 * m - 6 * (180 - 44 * m)/4 = 48
79 * m - 6 * (180 - 44 * m)/4 = 48
79 * m - 6 * (180 - 44 * m)/4 = 48
79 * m - 6 * (180 - 44 * m)/4 = 48
79 * m - 6 * (180 - 44 * m)/4 = 48
79 * m - 6 * (180 - 44 * m)/4 = 48
79 * m - 6 * (180 - 44 * m)/4 = 48
79 * m - 6 * (180 - 44 * m)/4 = 48
79 * m - 6 * (180 - 44 * m)/4 = 48
79 * m - 6 * (180 - 44 * m)/4 = 48
79 * m - 6 * (180 - 44 * m)/4 = 48
79 * m - 6 * (180 - 44 * m)/4 = 48
79 * m - 6 * (180 - 44 * m)/4 = 48
79 * m - 6 * (180 - 44 * m)/4 = 48
79 * m - 6 * (180 - 44 * m)/4 = 48
79 * m - 6 * (180 - 44 * m)/4 = 48
79 * m - 6 * (180 - 44 * m)/4 = 48
79 * m - 6 * (180 - 44 * m)/4 = 48
79 * m - 6 * (180 - 44 * m)/4 = 48
79 * m - 6 * (180 - 44 * m)/4 = 48
79 * m - 6 * (180 - 44 * m)/4 = 48
79 * m - 6 * (180 - 44 * m)/4 = 48
79 * m - 6 * (180 - 44 * m)/4 = 48
79 * m - 6 * (180 - 44 * m)/4 = 48
79 * m - 6 * (180 - 44 * m)/4 = 48
79 * m - 6 * (180 - 44 * m)/4 = 48
79 * m - 6 * (180 - 44 * m)/4 = 48
79 * m - 6 * (180 - 44 * m)/4 = 48
79 * m - 6 * (180 - 44 * m)/4 = 48
79 * m - 6 * (180 - 44 * m)/4 = 48
79 * m - 6 * (180 - 44 * m)/4 = 48
79 * m - 6 * (180 - 44 * m)/4 = 48
79 * m - 6 * (180 - 44 * m)/4 = 48
79 * m - 6 * (180 - 44 * m)/4 =

Expected answer: {b: 3027/145, m: 318/145}

Correct? No

🔗 Problem

Problem: Solve the following system of equations to find the values of o and g: 42 * o - 15 * g = 28 47 * o + 29 * g = 141.

Gemma 2B:

 Reasoning: 42 * o - 15 * g = 28
47 * o + 29 * g = 141

42 * o - 15 * g = 28
47 * o + 29 * g = 141

42 * o - 15 * g = 28
47 * o + 29 * g = 141

42 * o - 15 * g = 28
47 * o + 29 * g = 141

42 * o - 15 * g = 28
47 * o + 29 * g = 141

42 * o - 15 * g = 28
47 * o + 29 * g = 141

42 * o - 15 * g = 28
47 * o + 29 * g = 141

42 * o - 15 * g = 28
47 * o + 29 * g = 141

42 * o - 15 * g = 28
47 * o + 29 * g = 141

42 * o - 15 * g = 28
47 * o + 29 * g = 141

42 * o - 15 * g = 28
47 * o + 29 * g = 141

42 * o - 15 * g = 28
47 * o + 29 * g = 141

42 * o - 15 * g = 28
47 * o + 29 * g = 141

42 * o - 15 * g = 28
47 * o + 29 * g = 141

42 * o - 15 * g = 28
47 * o + 29 * g = 141

42 * o - 15 * g = 28
47 * o + 29 * g = 141

42 * o - 15 * g = 28
47 * o + 29 * g = 141

42 * o - 15 * g = 28
47 * o + 29 * g = 141

42 * o - 15 * g = 28
47 * o + 29 * g = 141

42 * o - 15 * g = 28
47 * o + 29 * g = 141

42 * o - 15 * g = 28
47 * o + 29 * g = 141

42 * o - 15 * g = 28
47 * o + 29 * g = 141

42 * o - 15 * g = 28
47 * o + 29 * g = 141

42 * o - 15 * g = 28
47 * o + 29 * g = 141

42 * o - 15 * g = 28
47 * o + 29 * g = 141

42 * o - 15 * g = 28
47 * o + 29 * g = 141

42 * o - 15 * g = 28
47 * o + 29 * g = 141

42 * o - 15 * g = 28
47 * o + 29 * g = 141

42 * o - 15 * g = 28
47 * o + 29 * g = 141

42 * o - 15 * g = 28
47 * o + 29 * g = 141

42 * o - 15 * g = 28
47 * o + 29 * g = 141

42 *

Expected answer: {g: 4606/1923, o: 2927/1923}

Correct? No

🔗 Problem

Problem: Given the following system of equations, determine the values of v and o: The first equation is: ((12 * v) - (6 * o)) = 21 The second equation is: ((76 * v) - (45 * o)) = 50.

Gemma 2B:

 Reasoning: 
The first equation is: ((12 * v) - (6 * o)) = 21
The second equation is:  ((76 * v) - (45 * o)) = 50.
### Answer: v = 1, o = 1

Expected answer: {o: 83/7, v: 215/28}

Correct? No

🔗 Problem

Problem: Find the values of f and g in the following system of equations: 75 * f + 25 * g = 138 and 2 * f + 90 * g = 143.

Gemma 2B:

 Reasoning: 75 * f + 25 * g = 138 and 2 * f + 90 * g = 143.
75 * f + 25 * g = 138
2 * f + 90 * g = 143
### Answer: f = 1, g = 1

Expected answer: {f: 1769/1340, g: 10449/6700}

Correct? No

🔗 Problem

Problem: Solve the following system of equations for variables y and n: the first equation is 194 = 4 * y + 14 * n and the second equation is 7 = 65 * n - 79 * y.

Gemma 2B:

 Reasoning: 194 = 4 * y + 14 * n
194 - 4 * y = 14 * n
<<194-4*y=14*n>>
7 = 65 * n - 79 * y
<<7=65*n-79*y>>
### Answer: y = <<y=1>>1, n = <<n=1>>1

Expected answer: {n: 7677/683, y: 6256/683}

Correct? No

🔗 Problem

Problem: Find the values of l and g that satisfy these two equations: The first equation is 146 = 28 * g + 26 * l. The second equation is 6 = 41 * l - 53 * g.

Gemma 2B:

 Reasoning: 
The first equation is 146 = 28 * g + 26 * l.
The second equation is 6 = 41 * l - 53 * g.
### Answer: l = 1, g = 1

Expected answer: {g: 2915/1263, l: 3953/1263}

Correct? No

🔗 Problem

Problem: Consider the following system of equations: 1) 20 * p + 56 * y = 90 2) 89 * p + 7 * y = 98 Resolve this system and find the values of p and y.

Gemma 2B:

 Reasoning: 1) 20 * p + 56 * y = 90
2) 89 * p + 7 * y = 98

Multiply the first equation by 7 and the second equation by 56.

7 * (20 * p + 56 * y = 90)
56 * (89 * p + 7 * y = 98)

7 * (20 * p) + 7 * (56 * y) = 7 * (90)
56 * (89 * p) + 56 * (7 * y) = 56 * (98)

140 * p + 392 * y = 630
4752 * p + 372 * y = 5328

Subtract the second equation from the first equation.

140 * p + 392 * y = 630
- (4752 * p + 372 * y = 5328)
--------------------------------
-4612 * p - 330 * y = -798

Divide both sides by -330.

-4612 * p - 330 * y = -798
-330 * y = -798
------------------
-4612 * p = 238

Divide both sides by -4612.

-4612 * p = 238
-4612 * p = 238
------------------
p = -0.052

Substitute p = -0.052 into the first equation.

1) 20 * p + 56 * y = 90
2) 89 * p + 7 * y = 98

1) 20 * (-0.052) + 56 * y = 90
2) 89 * (-0.052) + 7 * y = 98

-1.04 + 56 * y = 90
-0.478 + 7 * y = 98

56 * y = 89.96
7 * y = 98.03

Divide both sides by 56.

56 * y = 89.96
56 * y = 89.96
------------------
y = 1.62

Substitute y = 1.62 into the first equation.

1) 20 * p + 56 * y = 90
2) 89 * p + 7 * y = 98

1) 20 * p + 56 * (1.62) = 90
2) 89 * p + 7 * (1.62) = 98

20 * p + 90.56 = 90
89 * p + 11.44 = 98

20 * p = -9.56
89 * p = 9.56

Divide both sides by 20.

20 * p = -9.56
20 * p = -9.56
------------------
p = -0.478

Substitute p = -0.478 into the first equation.

1) 20 * p + 56 * y = 90
2) 89 * p + 7 * y = 98

1) 20 * (-0.478) + 56 * y = 90
2) 89 * (-0.478) + 7 * y = 98

-9.56 + 56 * y = 90
-42.02 + 7 * y = 98

56 * y = 99.56
7 * y = 56.02

Divide both sides by 56.

56 * y = 99.56
56 * y = 99.56
------------------
y = 1.81

Expected answer: {p: 347/346, y: 3025/2422}

Correct? No

🔗 Problem

Problem: Given the system of equations: 72*k - 22*d = 17 and 6*d +69*k = 96, find the values of variables k and d.

Gemma 2B:

 Reasoning: 72*k - 22*d = 17 and 6*d +69*k = 96
72*k - 22*d = 17
6*d +69*k = 96
### Answer: k = 1, d = 2

Expected answer: {d: 1913/650, k: 369/325}

Correct? No

🔗 Problem

Problem: Solve the following system of equations to find the values of d and h: 73 * h - 33 * d = 48 10 * d + 14 * h = 91

Gemma 2B:

 Reasoning:

73 * h - 33 * d = 48

10 * d + 14 * h = 91

73 * h - 33 * d = 48

10 * d + 14 * h = 91

73 * h - 33 * d = 48

10 * d + 14 * h = 91

73 * h - 33 * d = 48

10 * d + 14 * h = 91

73 * h - 33 * d = 48

10 * d + 14 * h = 91

73 * h - 33 * d = 48

10 * d + 14 * h = 91

73 * h - 33 * d = 48

10 * d + 14 * h = 91

73 * h - 33 * d = 48

10 * d + 14 * h = 91

73 * h - 33 * d = 48

10 * d + 14 * h = 91

73 * h - 33 * d = 48

10 * d + 14 * h = 91

73 * h - 33 * d = 48

10 * d + 14 * h = 91

73 * h - 33 * d = 48

10 * d + 14 * h = 91

73 * h - 33 * d = 48

10 * d + 14 * h = 91

73 * h - 33 * d = 48

10 * d + 14 * h = 91

73 * h - 33 * d = 48

10 * d + 14 * h = 91

73 * h - 33 * d = 48

10 * d + 14 * h = 91

73 * h - 33 * d = 48

10 * d + 14 * h = 91

73 * h - 33 * d = 48

10 * d + 14 * h = 91

73 * h - 33 * d = 48

10 * d + 14 * h = 91

73 * h - 33 * d = 48

10 * d + 14 * h = 91

73 * h - 33 * d = 48

10 * d + 14 * h = 91

73 * h - 33 * d = 48

10 * d + 14 * h = 91

73 * h - 33 * d = 48

10 * d + 14 * h = 91

73 * h - 33 * d = 48

10 * d + 14 * h = 91

73 * h - 33 * d = 48

10 * d + 14 * h = 91

73 * h - 33 * d = 48

10 * d + 14 * h = 91

73 * h - 33 * d = 48

10 * d + 14 * h = 91

73 * h - 33 * d = 48

10 * d + 14 * h = 91

73 * h - 33 * d = 48

10 * d + 14 * h = 91

73 * h - 33 * d = 48

10 * d + 14 * h = 91

73 * h - 33 * d = 48

10 * d + 14 * h = 91

73

Expected answer: {d: 5971/1192, h: 3483/1192}

Correct? No

🔗 Problem

Problem: Solve the following system of equations for the values of q and e: 1) 43 * q - 44 * e = 29 2) 30 * q + 43 * e = 130

Gemma 2B:

 Reasoning: 

1) 43 * q - 44 * e = 29
2) 30 * q + 43 * e = 130

Multiply equation 1 by 43 and equation 2 by 44:

43 * 43 * q - 44 * 43 * e = 43 * 29
30 * 43 * q + 43 * 44 * e = 130 * 44

Simplify:

1849 * q - 1844 * e = 1213
30 * 43 * q + 43 * 44 * e = 5520

Multiply equation 1 by 44 and equation 2 by 43:

1849 * 44 * q - 1844 * 44 * e = 1213 * 44
30 * 43 * 43 * q + 43 * 44 * 43 * e = 5520 * 43

Simplify:

81116 * q - 81152 * e = 52124
30 * 43 * 43 * q + 43 * 44 * 43 * e = 239120

Multiply equation 1 by 43 and equation 2 by 44:

81116 * 43 * q - 81152 * 43 * e = 52124 * 43
30 * 43 * 43 * 43 * q + 43 * 44 * 43 * 43 * e = 239120 * 44

Simplify:

3501152 * q - 3501986 * e = 2218452
30 * 43 * 43 * 43 * q + 43 * 44 * 43 * 43 * e = 10368800

Multiply equation 1 by 44 and equation 2 by 43:

3501152 * 44 * q - 3501986 * 44 * e = 2218452 * 44
30 * 43 * 43 * 43 * 43 * q + 43 * 44 * 43 * 43 * 43 * e = 10368800 * 43

Simplify:

15005664 * q - 15023876 * e = 9323728
30 * 43 * 43 * 43 * 43 * q + 43 * 44 * 43 * 43 * 43 * e = 43144000

Multiply equation 1 by 43 and equation 2 by 44:

15005664 * 43 * q - 15023876 * 43 * e = 9323728 * 43
30 * 43 * 43 * 43 * 43 * 43 * q + 43 * 44 * 43 * 43 * 43 * 43 * e = 43144000 * 44

Simplify:

675309952 * q - 676274888 * e = 40391244
30 * 43 * 43 * 43 * 43 * 43 * q + 43 * 44 * 43 * 43 * 43 * 43 * e = 1843200000

Multiply equation 1 by 44 and equation 2 by 43:

675309952 *

Expected answer: {e: 4720/3169, q: 6967/3169}

Correct? No

🔗 Problem

Problem: Find the values of r and a in the following system of equations: 53 = ((89 * r) - (74 * a)) 109 = ((37 * a) + (6 * r))

Gemma 2B:

 Reasoning: 

53 = ((89 * r) - (74 * a))
109 = ((37 * a) + (6 * r))

53 = 89 * r - 74 * a
109 = 37 * a + 6 * r

53 + 74 * a = 89 * r
109 - 6 * r = 37 * a

53 + 74 * a = 89 * r
109 - 6 * r = 37 * a

53 + 74 * a = 89 * r
109 - 6 * r = 37 * a

53 + 74 * a = 89 * r
109 - 6 * r = 37 * a

53 + 74 * a = 89 * r
109 - 6 * r = 37 * a

53 + 74 * a = 89 * r
109 - 6 * r = 37 * a

53 + 74 * a = 89 * r
109 - 6 * r = 37 * a

53 + 74 * a = 89 * r
109 - 6 * r = 37 * a

53 + 74 * a = 89 * r
109 - 6 * r = 37 * a

53 + 74 * a = 89 * r
109 - 6 * r = 37 * a

53 + 74 * a = 89 * r
109 - 6 * r = 37 * a

53 + 74 * a = 89 * r
109 - 6 * r = 37 * a

53 + 74 * a = 89 * r
109 - 6 * r = 37 * a

53 + 74 * a = 89 * r
109 - 6 * r = 37 * a

53 + 74 * a = 89 * r
109 - 6 * r = 37 * a

53 + 74 * a = 89 * r
109 - 6 * r = 37 * a

53 + 74 * a = 89 * r
109 - 6 * r = 37 * a

53 + 74 * a = 89 * r
109 - 6 * r = 37 * a

53 + 74 * a = 89 * r
109 - 6 * r = 37 * a

53 + 74 * a = 89 * r
109 - 6 * r = 37 * a

53 + 74 * a = 89 * r
109 - 6 * r = 37 * a

53 + 74 * a = 89 * r
109 - 6 * r = 37 * a

53 + 74 * a = 89 * r
109 - 6 * r = 37 * a

53 + 74 * a = 89 * r
109 - 6 * r = 37 * a

53 + 74 * a = 89 * r
109 - 6 * r = 37 * a

53 + 74 * a = 89 * r
109 - 6 * r = 37 * a

53 + 74 * a = 89 * r
109 - 6 * r = 37 * a

53 + 74 * a = 89 * r
109 - 6 * r = 37 * a

53 + 74 * a = 89 * r
109 - 6 * r = 37 * a

53 + 74 * a = 89 * r
109 - 6 * r = 37 *

Expected answer: {a: 9383/3737, r: 271/101}

Correct? No

🔗 Problem

Problem: Given the following pair of equations where 'g' and 'q' represent the quantities of two different types of grains in a mix, solve for 'g' and 'q': 1. The sum of the weights of 42 units of 'g' and 12 units of 'q' equals 169 kg. 2. The weight of 12 units of 'q' minus the weight of 50 units of 'g' results in 19 kg.

Gemma 2B:

 Reasoning:

1. g + q = 169
2. q - 50g = 19

Multiply the first equation by 50 and the second equation by 1:

50g + 50q = 8450
q - 50g = 19

Subtract the second equation from the first equation:

51q = 8261

Divide both sides by 51:

q = 162

Substitute q = 162 into the first equation:

g + 162 = 169

Subtract 162 from both sides:

g = 7

### Answer: g = 7, q = 162

Expected answer: {g: 75/46, q: 578/69}

Correct? No

🔗 Problem

Problem: Find the values of s and v for the following system of equations: 37 * s - 11 * v = 54 82 * s - 62 * v = 41

Gemma 2B:

 Reasoning: 37 * s - 11 * v = 54
37 * s - 11 * v = 54
82 * s - 62 * v = 41
### Answer: s = 1, v = 2

Expected answer: {s: 2897/1392, v: 2911/1392}

Correct? No

🔗 Problem

Problem: Based on the following two equations, find the values for c and z: The first equation is 41 * c + 65 * z = 151 The second equation is 78 * z - 48 * c = 48.

Gemma 2B:

 Reasoning: 

The first equation is 41 * c + 65 * z = 151
The second equation is 78 * z - 48 * c = 48.

The first equation is 41 * c + 65 * z = 151
The second equation is 78 * z - 48 * c = 48.

The first equation is 41 * c + 65 * z = 151
The second equation is 78 * z - 48 * c = 48.

The first equation is 41 * c + 65 * z = 151
The second equation is 78 * z - 48 * c = 48.

The first equation is 41 * c + 65 * z = 151
The second equation is 78 * z - 48 * c = 48.

The first equation is 41 * c + 65 * z = 151
The second equation is 78 * z - 48 * c = 48.

The first equation is 41 * c + 65 * z = 151
The second equation is 78 * z - 48 * c = 48.

The first equation is 41 * c + 65 * z = 151
The second equation is 78 * z - 48 * c = 48.

The first equation is 41 * c + 65 * z = 151
The second equation is 78 * z - 48 * c = 48.

The first equation is 41 * c + 65 * z = 151
The second equation is 78 * z - 48 * c = 48.

The first equation is 41 * c + 65 * z = 151
The second equation is 78 * z - 48 * c = 48.

The first equation is 41 * c + 65 * z = 151
The second equation is 78 * z - 48 * c = 48.

The first equation is 41 * c + 65 * z = 151
The second equation is 78 * z - 48 * c = 48.

The first equation is 41 * c + 65 * z = 151
The second equation is 78 * z - 48 * c = 48.

The first equation is 41 * c + 65 * z = 151
The second equation is 78 * z - 48 * c = 48.

The first equation is 41 * c + 65 * z = 151
The second equation is 78 * z - 48 * c = 48.

The first equation is 41 * c + 65 * z = 151
The second equation is 78 * z - 48 * c = 48.

The first equation is 41 * c + 65 * z = 151
The second equation is 78 * z - 48 * c = 48.

The first equation is 41 * c + 65 * z = 151
The second equation is 78 * z - 48 * c = 48.

The first equation is 41 * c + 65 * z = 151
The second equation is 78 * z - 48 * c = 48.

The first equation is 41 * c + 65 * z = 151
The second equation is 78 * z - 48 * c = 48.

The first equation is 41 * c + 65 * z = 151
The second equation is 78 * z - 48 * c = 48.

The first equation is 41 * c + 65 * z = 151
The second equation is 78 * z - 48 * c = 48.

The first equation is

Expected answer: {c: 37/27, z: 512/351}

Correct? No

🔗 Problem

Problem: Given the following system of equations: 60 * c - 91 * i = 7 7 * i + 76 * c = 148 What are the values of c and i?

Gemma 2B:

 Reasoning: 60 * c - 91 * i = 7
7 * i + 76 * c = 148

7 * i + 76 * c = 148
- 60 * c - 91 * i = 7
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Expected answer: {c: 1931/1048, i: 2087/1834}

Correct? No

🔗 Problem

Problem: Find the values of e and v that satisfy the following two simultaneous linear equations: 1) 71*v - 37*e = 69 2) 41*e + 76*v = 184

Gemma 2B:

 Reasoning: 

1) 71*v - 37*e = 69
2) 41*e + 76*v = 184

Multiply equation 1 by 41 and equation 2 by 37:

41*71*v - 41*37*e = 41*69
37*41*e + 37*76*v = 37*184

Subtract the two equations:

(41*71*v - 41*37*e) - (37*41*e + 37*76*v) = 41*69 - 37*184

Simplify:

(41*71*v - 41*37*e) - (37*41*e + 37*76*v) = 41*69 - 37*184

41*71*v - 41*37*e - 37*41*e - 37*76*v = 41*69 - 37*184

41*71*v - 41*37*e - 37*41*e - 37*76*v = 41*69 - 37*184

41*71*v - 41*37*e - 37*41*e - 37*76*v = 41*69 - 37*184

41*71*v - 41*37*e - 37*41*e - 37*76*v = 41*69 - 37*184

41*71*v - 41*37*e - 37*41*e - 37*76*v = 41*69 - 37*184

41*71*v - 41*37*e - 37*41*e - 37*76*v = 41*69 - 37*184

41*71*v - 41*37*e - 37*41*e - 37*76*v = 41*69 - 37*184

41*71*v - 41*37*e - 37*41*e - 37*76*v = 41*69 - 37*184

41*71*v - 41*37*e - 37*41*e - 37*76*v = 41*69 - 37*184

41*71*v - 41*37*e - 37*41*e - 37*76*v = 41*69 - 37*184

41*71*v - 41*37*e - 37*41*e - 37*76*v = 41*69 - 37*184

41*71*v - 41*37*e - 37*41*e - 37*76*v = 41*69 - 37*184

41*71*v - 41*37*e - 37*41*e - 37*76*v = 41*69 - 37*184

41*71*v - 41*37*e - 37*41*e - 37*76*v = 41*69 - 37*184

41*71*v - 41*37*e - 37*41*e - 37*76*v = 41*69 - 37*1

Expected answer: {e: 7820/5723, v: 9637/5723}

Correct? No

🔗 Problem

Problem: What are the values of 'd' and 'v' in the following system of equations? The sum of 25 times 'v' and 69 times 'd' equals 113. The sum of 26 times 'd' and 42 times 'v' equals 85.

Gemma 2B:

 Reasoning: 25v+69d=113
26d+42v=85

25v+69d=113
26d+42v=85

25v+69d=113
26d+42v=85

25v+69d=113
26d+42v=85

25v+69d=113
26d+42v=85

25v+69d=113
26d+42v=85

25v+69d=113
26d+42v=85

25v+69d=113
26d+42v=85

25v+69d=113
26d+42v=85

25v+69d=113
26d+42v=85

25v+69d=113
26d+42v=85

25v+69d=113
26d+42v=85

25v+69d=113
26d+42v=85

25v+69d=113
26d+42v=85

25v+69d=113
26d+42v=85

25v+69d=113
26d+42v=85

25v+69d=113
26d+42v=85

25v+69d=113
26d+42v=85

25v+69d=113
26d+42v=85

25v+69d=113
26d+42v=85

25v+69d=113
26d+42v=85

25v+69d=113
26d+42v=85

25v+69d=113
26d+42v=85

25v+69d=113
26d+42v=85

25v+69d=113
26d+42v=85

25v+69d=113
26d+42v=85

25v+69d=113
26d+42v=85

25v+69d=113
26d+42v=85

25v+69d=113
26d+42v=85

25v+69d=113
26d+42v=85

25v+69d=113
26d+42v=85

25v+69d=113
26d+42v=85

25v+69d=113
26d+42v=85

25v+69d=113
26d+42v=85

25v+69d=113
26d+42v=85

25v+69d=113
26d+42v=85

25v+69d=113
26d+42v=85

25v+69d=113
26d+42v=85

25v+69d=113
26d+42v=85

25v+69d=113
26d+42v=85

25v+69d=113
26d+42v=85

25v+69d=113

Expected answer: {d: 2621/2248, v: 2927/2248}

Correct? No

🔗 Problem

Problem: Solve the following equations for g and z: 43 * z - 91 * g = 33 72 * g - 3 * z = 68

Gemma 2B:

 Reasoning: 

43 * z - 91 * g = 33
72 * g - 3 * z = 68

43 * z - 91 * g = 33
72 * g - 3 * z = 68

43 * z - 91 * g = 33
72 * g - 3 * z = 68

43 * z - 91 * g = 33
72 * g - 3 * z = 68

43 * z - 91 * g = 33
72 * g - 3 * z = 68

43 * z - 91 * g = 33
72 * g - 3 * z = 68

43 * z - 91 * g = 33
72 * g - 3 * z = 68

43 * z - 91 * g = 33
72 * g - 3 * z = 68

43 * z - 91 * g = 33
72 * g - 3 * z = 68

43 * z - 91 * g = 33
72 * g - 3 * z = 68

43 * z - 91 * g = 33
72 * g - 3 * z = 68

43 * z - 91 * g = 33
72 * g - 3 * z = 68

43 * z - 91 * g = 33
72 * g - 3 * z = 68

43 * z - 91 * g = 33
72 * g - 3 * z = 68

43 * z - 91 * g = 33
72 * g - 3 * z = 68

43 * z - 91 * g = 33
72 * g - 3 * z = 68

43 * z - 91 * g = 33
72 * g - 3 * z = 68

43 * z - 91 * g = 33
72 * g - 3 * z = 68

43 * z - 91 * g = 33
72 * g - 3 * z = 68

43 * z - 91 * g = 33
72 * g - 3 * z = 68

43 * z - 91 * g = 33
72 * g - 3 * z = 68

43 * z - 91 * g = 33
72 * g - 3 * z = 68

43 * z - 91 * g = 33
72 * g - 3 * z = 68

43 * z - 91 * g = 33
72 * g - 3 * z = 68

43 * z - 91 * g = 33
72 * g - 3 * z = 68

43 * z - 91 * g = 33
72 * g - 3 * z = 68

43 * z - 91 * g = 33
72 * g - 3 * z = 68

43 * z - 91 * g = 33
72 * g - 3 * z = 68

43 * z - 91 * g = 33
72 * g - 3 * z = 68

43 * z - 91 * g = 33
72 * g - 3 * z = 68

43 * z - 91 * g = 33
72 * g - 3 * z = 68

43 * z - 91 * g = 33
72 * g - 3 * z = 68

43 * z - 91 * g = 33
72 * g - 3 * z = 68

43 *

Expected answer: {g: 3023/2823, z: 8564/2823}

Correct? No

🔗 Problem

Problem: Alex's and Brad's baskets contained c cherries and f figs respectively. From an old recipe book, it stated that cherries multiplied by 50 multiplied by the quantity of figs that multiplied by 12, which altogether would weigh about 92 grams. Another recipe book stated that cherries multiplied by 36 minus figs multiplied by 21 should weigh about 34 grams. Can you find the quantity of cherries (c) and figs (f)? Use the following system of equations to solve: 50c + 12f = 92 36c - 21f = 34.

Gemma 2B:

 Reasoning: 50c + 12f = 92
50c = 92 - 12f
c = (92 - 12f)/50

36c - 21f = 34
36c = 34 + 21f
c = (34 + 21f)/36

c = (92 - 12f)/50 = (34 + 21f)/36

36(92 - 12f) = 50(34 + 21f)
3296 - 368f = 1700 + 1050f
1700 + 1050f = 3296 - 368f
1700 + 1050f + 368f = 3296
1050f + 368f = 3296 - 1700
1418f = 1596
f = 1596/1418
f = 1.08

c = (92 - 12f)/50
c = (92 - 12(1.08))/50
c = (92 - 12.96)/50
c = 79.04/50
c = 1.58

### Answer: 1.58, 1.08

Expected answer: {c: 30/19, f: 62/57}

Correct? No

🔗 Problem

Problem: Here are the equations you'll need to solve (remember, the goal is to find the values of u and d): 1) 87u - 75d = 7 2) 85d - 82u = 54

Gemma 2B:

 Reasoning: We can solve this system of equations using substitution.

Let's start by solving the first equation for u:

87u - 75d = 7
87u = 75d + 7
u = (75d + 7)/87

Now, let's substitute (75d + 7)/87 for u in the second equation:

85d - 82u = 54
85d - 82((75d + 7)/87) = 54
85d - (82(75d + 7))/87 = 54
85d - (82(75d))/87 - (82(7))/87 = 54
85d - (6500d)/87 - (574)/87 = 54
(85(87)d - 6500d - 574)/87 = 54
(7495d - 6500d - 574)/87 = 54
(795d - 574)/87 = 54
795d = 54(87) + 574
795d = 4908 + 574
795d = 5482
d = 5482/795
d = 7

Now, let's substitute 7 for d in the first equation:

87u - 75d = 7
87u - 75(7) = 7
87u - 525 = 7
87u = 525 + 7
87u = 532
u = 532/87
u = 6

### Answer: u = 6, d = 7

Expected answer: {d: 5272/1245, u: 929/249}

Correct? No

🔗 Problem

Problem: Bill is trying to decipher a secret code. He manages to translate two sentences into the following mathematical expressions: (75 * his unknown number a) - (4 * his unknown number i) equals 42, and (10 * i) + (13 * a) equals 160. Using these equations, can you figure out the values of i and a for him?

Gemma 2B:

 Reasoning: (75 * a) - (4 * i) = 42
(75 * a) - (4 * i) = 42
(10 * i) + (13 * a) = 160
### Answer: a = 16, i = 10

Expected answer: {a: 530/401, i: 5727/401}

Correct? No

🔗 Problem

Problem: Solve the following system of equations for the values of p and c: 37 * p + 74 * c = 183 27 * c - 18 * p = 13

Gemma 2B:

 Reasoning: 37 * p + 74 * c = 183
27 * c - 18 * p = 13

37 * p + 74 * c = 183
27 * c - 18 * p = 13

37 * p + 74 * c = 183
27 * c - 18 * p = 13

37 * p + 74 * c = 183
27 * c - 18 * p = 13

37 * p + 74 * c = 183
27 * c - 18 * p = 13

37 * p + 74 * c = 183
27 * c - 18 * p = 13

37 * p + 74 * c = 183
27 * c - 18 * p = 13

37 * p + 74 * c = 183
27 * c - 18 * p = 13

37 * p + 74 * c = 183
27 * c - 18 * p = 13

37 * p + 74 * c = 183
27 * c - 18 * p = 13

37 * p + 74 * c = 183
27 * c - 18 * p = 13

37 * p + 74 * c = 183
27 * c - 18 * p = 13

37 * p + 74 * c = 183
27 * c - 18 * p = 13

37 * p + 74 * c = 183
27 * c - 18 * p = 13

37 * p + 74 * c = 183
27 * c - 18 * p = 13

37 * p + 74 * c = 183
27 * c - 18 * p = 13

37 * p + 74 * c = 183
27 * c - 18 * p = 13

37 * p + 74 * c = 183
27 * c - 18 * p = 13

37 * p + 74 * c = 183
27 * c - 18 * p = 13

37 * p + 74 * c = 183
27 * c - 18 * p = 13

37 * p + 74 * c = 183
27 * c - 18 * p = 13

37 * p + 74 * c = 183
27 * c - 18 * p = 13

37 * p + 74 * c = 183
27 * c - 18 * p = 13

37 * p + 74 * c = 183
27 * c - 18 * p = 13

37 * p + 74 * c = 183
27 * c - 18 * p = 13

37 * p + 74 * c = 183
27 * c - 18 * p = 13

37 * p + 74 * c = 183
27 * c - 18 * p = 13

37 * p + 74 * c = 183
27 * c - 18 * p = 13

37 * p + 74 * c = 183
27 * c - 18 * p = 13

37 * p + 74 * c = 183
27 * c - 18 * p = 13

37 * p + 74 * c = 183
27 * c - 18 * p = 13

37 *

Expected answer: {c: 3775/2331, p: 3979/2331}

Correct? No

🔗 Problem

Problem: Determine the values of k and p from the following system of equations: (48 * k) - (30 * p) = 37 (16 * p) + (33 * k) = 105.

Gemma 2B:

 Reasoning:
(48 * k) - (30 * p) = 37
(16 * p) + (33 * k) = 105
(48 * k) - (30 * p) = 37
(16 * p) + (33 * k) = 105
(48 * k) - (30 * p) = 37
(16 * p) + (33 * k) = 105
(48 * k) - (30 * p) = 37
(16 * p) + (33 * k) = 105
(48 * k) - (30 * p) = 37
(16 * p) + (33 * k) = 105
(48 * k) - (30 * p) = 37
(16 * p) + (33 * k) = 105
(48 * k) - (30 * p) = 37
(16 * p) + (33 * k) = 105
(48 * k) - (30 * p) = 37
(16 * p) + (33 * k) = 105
(48 * k) - (30 * p) = 37
(16 * p) + (33 * k) = 105
(48 * k) - (30 * p) = 37
(16 * p) + (33 * k) = 105
(48 * k) - (30 * p) = 37
(16 * p) + (33 * k) = 105
(48 * k) - (30 * p) = 37
(16 * p) + (33 * k) = 105
(48 * k) - (30 * p) = 37
(16 * p) + (33 * k) = 105
(48 * k) - (30 * p) = 37
(16 * p) + (33 * k) = 105
(48 * k) - (30 * p) = 37
(16 * p) + (33 * k) = 105
(48 * k) - (30 * p) = 37
(16 * p) + (33 * k) = 105
(48 * k) - (30 * p) = 37
(16 * p) + (33 * k) = 105
(48 * k) - (30 * p) = 37
(16 * p) + (33 * k) = 105
(48 * k) - (30 * p) = 37
(16 * p) + (33 * k) = 105
(48 * k) - (30 * p) = 37
(16 * p) + (33 * k) = 105
(48 * k) - (30 * p) = 37
(16 * p) + (33 * k) = 105
(48 * k) - (30 * p) = 37
(16 * p) + (33 * k) = 105
(48 * k) - (30 * p) = 37
(16 * p) + (33 * k) = 105
(48 * k) - (30 * p) = 37
(16 * p) + (33 * k) = 105
(48 * k) - (30 * p) = 37
(16 * p) + (33 * k) = 105
(48 * k) - (30 * p) = 37
(16 * p) + (33 * k) = 105
(48 * k) - (30 * p) = 37
(16 * p) + (33 * k) = 

Expected answer: {k: 1871/879, p: 1273/586}

Correct? No

🔗 Problem

Problem: Consider the following pair of equations. 1. 75v - 69f = 14 2. 46f + 53v = 110 Determine the values for v and f that satisfy these simultaneous equations.

Gemma 2B:

 Reasoning: 75v - 69f = 14
75v = 14 + 69f
v = (14 + 69f)/75

46f + 53v = 110
46f + 53((14 + 69f)/75) = 110
46f + 14 + 69f = 110
115f = 110 - 14
115f = 96
f = 96/115 = <<96/115=0.836>>0.836

75v - 69(0.836) = 14
75v - 57.91 = 14
75v = 14 + 57.91
75v = 71.91
v = 71.91/75 = <<71.91/75=0.955>>0.955

### Answer: v = 0.955, f = 0.836

Expected answer: {f: 7508/7107, v: 358/309}

Correct? No

🔗 Problem

Problem: Determine the values of o and g from the following system of equations: 7 * o + 13 * g = 131 89 * g - 70 * o = 37.

Gemma 2B:

 Reasoning: 7 * o + 13 * g = 131
89 * g - 70 * o = 37
### Answer: o = 1, g = 2

Expected answer: {g: 449/73, o: 3726/511}

Correct? No

🔗 Problem

Problem: Solve the following system of equations for the values of d and k: 88 * d - 60 * k = 38 33 * k - 11 * d = 46.

Gemma 2B:

 Reasoning: 88 * d - 60 * k = 38
33 * k - 11 * d = 46
### Answer: d = 1, k = 2

Expected answer: {d: 669/374, k: 203/102}

Correct? No

🔗 Problem

Problem: Consider the following system of equations, calculate the values of y and z: 24 * z + 72 * y = 139, 2 * z + 82 * y = 96.

Gemma 2B:

 Reasoning: 24 * z + 72 * y = 139
2 * z + 82 * y = 96

24 * z + 72 * y = 139
2 * z + 82 * y = 96

24 * z + 72 * y = 139
2 * z + 82 * y = 96

24 * z + 72 * y = 139
2 * z + 82 * y = 96

24 * z + 72 * y = 139
2 * z + 82 * y = 96

24 * z + 72 * y = 139
2 * z + 82 * y = 96

24 * z + 72 * y = 139
2 * z + 82 * y = 96

24 * z + 72 * y = 139
2 * z + 82 * y = 96

24 * z + 72 * y = 139
2 * z + 82 * y = 96

24 * z + 72 * y = 139
2 * z + 82 * y = 96

24 * z + 72 * y = 139
2 * z + 82 * y = 96

24 * z + 72 * y = 139
2 * z + 82 * y = 96

24 * z + 72 * y = 139
2 * z + 82 * y = 96

24 * z + 72 * y = 139
2 * z + 82 * y = 96

24 * z + 72 * y = 139
2 * z + 82 * y = 96

24 * z + 72 * y = 139
2 * z + 82 * y = 96

24 * z + 72 * y = 139
2 * z + 82 * y = 96

24 * z + 72 * y = 139
2 * z + 82 * y = 96

24 * z + 72 * y = 139
2 * z + 82 * y = 96

24 * z + 72 * y = 139
2 * z + 82 * y = 96

24 * z + 72 * y = 139
2 * z + 82 * y = 96

24 * z + 72 * y = 139
2 * z + 82 * y = 96

24 * z + 72 * y = 139
2 * z + 82 * y = 96

24 * z + 72 * y = 139
2 * z + 82 * y = 96

24 * z + 72 * y = 139
2 * z + 82 * y = 96

24 * z + 72 * y = 139
2 * z + 82 * y = 96

24 * z + 72 * y = 139
2 * z + 82 * y = 96

24 * z + 72 * y = 139
2 * z + 82 * y = 96

24 * z + 72 * y = 139
2 * z + 82 * y = 96

24 * z + 72 * y = 139
2 * z + 82 * y = 96

24 * z + 72 * y = 139
2 * z + 82 * y = 96

24 * z + 72 * y = 139
2 * z + 82 * y = 96

24 *

Expected answer: {y: 1013/912, z: 2243/912}

Correct? No

🔗 Problem

Problem: Solve the following system of equations for the variables v and o: (87 * o) - (29 * v) = 1 and (8 * v) + (30 * o) = 91.

Gemma 2B:

 Reasoning: (87 * o) - (29 * v) = 1 and (8 * v) + (30 * o) = 91.
(87 * o) - (29 * v) = 1
(8 * v) + (30 * o) = 91
### Answer: v = 1, o = 3

Expected answer: {o: 2647/1566, v: 2629/522}

Correct? No

🔗 Problem

Problem: Solve the following system of equations for h and p: The first equation is (23 * h) - (46 * p) = 58 The second equation is (11 * p) + (23 * h) = 124.

Gemma 2B:

 Reasoning: The first equation is (23 * h) - (46 * p) = 58.
The second equation is (11 * p) + (23 * h) = 124.

(23 * h) - (46 * p) = 58
(11 * p) + (23 * h) = 124

(23 * h) - (46 * p) = 58
(11 * p) + (23 * h) = 124

(23 * h) - (46 * p) = 58
(11 * p) + (23 * h) = 124

(23 * h) - (46 * p) = 58
(11 * p) + (23 * h) = 124

(23 * h) - (46 * p) = 58
(11 * p) + (23 * h) = 124

(23 * h) - (46 * p) = 58
(11 * p) + (23 * h) = 124

(23 * h) - (46 * p) = 58
(11 * p) + (23 * h) = 124

(23 * h) - (46 * p) = 58
(11 * p) + (23 * h) = 124

(23 * h) - (46 * p) = 58
(11 * p) + (23 * h) = 124

(23 * h) - (46 * p) = 58
(11 * p) + (23 * h) = 124

(23 * h) - (46 * p) = 58
(11 * p) + (23 * h) = 124

(23 * h) - (46 * p) = 58
(11 * p) + (23 * h) = 124

(23 * h) - (46 * p) = 58
(11 * p) + (23 * h) = 124

(23 * h) - (46 * p) = 58
(11 * p) + (23 * h) = 124

(23 * h) - (46 * p) = 58
(11 * p) + (23 * h) = 124

(23 * h) - (46 * p) = 58
(11 * p) + (23 * h) = 124

(23 * h) - (46 * p) = 58
(11 * p) + (23 * h) = 124

(23 * h) - (46 * p) = 58
(11 * p) + (23 * h) = 124

(23 * h) - (46 * p) = 58
(11 * p) + (23 * h) = 124

(23 * h) - (46 * p) = 58
(11 * p) + (23 * h) = 124

(23 * h) - (46 * p) = 58
(11 * p) + (23 * h) = 124

(23 * h) - (46 * p) = 58
(11 * p) + (23 * h) = 124

(23 * h) - (46 * p) = 58
(11 * p) + (23 * h) = 124

(23 * h) - (46 * p) = 58
(11 * p) + (23 * h) = 124

(23 * h) - (46 * p) = 58
(11 * p) + (23 * h) = 124

Expected answer: {h: 2114/437, p: 22/19}

Correct? No

🔗 Problem

Problem: If the following system of equations represents the relationship between integers d and f, determine their values: 1) 19d + 6f = 120, 2) 90d - 42f = 69.

Gemma 2B:

 Reasoning: 1) 19d + 6f = 120, 
2) 90d - 42f = 69.

1) 19d + 6f = 120, 
2) 90d - 42f = 69.

1) 19d + 6f = 120, 
2) 90d - 42f = 69.

1) 19d + 6f = 120, 
2) 90d - 42f = 69.

1) 19d + 6f = 120, 
2) 90d - 42f = 69.

1) 19d + 6f = 120, 
2) 90d - 42f = 69.

1) 19d + 6f = 120, 
2) 90d - 42f = 69.

1) 19d + 6f = 120, 
2) 90d - 42f = 69.

1) 19d + 6f = 120, 
2) 90d - 42f = 69.

1) 19d + 6f = 120, 
2) 90d - 42f = 69.

1) 19d + 6f = 120, 
2) 90d - 42f = 69.

1) 19d + 6f = 120, 
2) 90d - 42f = 69.

1) 19d + 6f = 120, 
2) 90d - 42f = 69.

1) 19d + 6f = 120, 
2) 90d - 42f = 69.

1) 19d + 6f = 120, 
2) 90d - 42f = 69.

1) 19d + 6f = 120, 
2) 90d - 42f = 69.

1) 19d + 6f = 120, 
2) 90d - 42f = 69.

1) 19d + 6f = 120, 
2) 90d - 42f = 69.

1) 19d + 6f = 120, 
2) 90d - 42f = 69.

1) 19d + 6f = 120, 
2) 90d - 42f = 69.

1) 19d + 6f = 120, 
2) 90d - 42f = 69.

1) 19d + 6f = 120, 
2) 90d - 42f = 69.

1) 19d + 6f = 120, 
2) 90d - 42f = 69.

1) 19d + 6f = 120, 
2) 90d - 42f = 69.

1) 19d + 6f = 120, 
2) 90d - 42f = 69.

1) 19d + 6f = 120, 
2) 90d - 42f = 69.

1) 19d + 6f = 120, 
2) 90d - 42f = 69.

1) 19d + 6f = 120, 
2) 90

Expected answer: {d: 909/223, f: 3163/446}

Correct? No

🔗 Problem

Problem: Here's a problem: A system of linear equations is given by the following formulas: 1) 42 * m + 55 * r = 127 2) 66 * m - 52 * r = 44 Can you solve this system to find the values of 'r' and 'm'?

Gemma 2B:

 Reasoning: 

1) 42 * m + 55 * r = 127 
2) 66 * m - 52 * r = 44 

Multiply equation 1 by 52 and equation 2 by 55 to get: 

52 * (42 * m + 55 * r = 127) 
55 * (66 * m - 52 * r = 44) 

52 * (42 * m) + 52 * (55 * r) = 52 * (127) 
55 * (66 * m) - 55 * (52 * r) = 55 * (44) 

2184 * m + 2840 * r = 6628 
3330 * m - 2840 * r = 2220 

Add equation 1 to equation 2 to get: 

2184 * m + 2840 * r = 6628 
3330 * m - 2840 * r = 2220 
--------------------------------
5510 * m = 8848 

Divide both sides by 5510 to get: 

m = 1.6129032258064516 

Substitute m = 1.6129032258064516 into equation 1 to get: 

42 * (1.6129032258064516) + 55 * r = 127 

Multiply both sides by 100 to get: 

42 * (1.6129032258064516 * 100) + 55 * r = 127 * 100 

42 * (161.29032258064516) + 55 * r = 12700 

42 * (161.29032258064516) + 55 * r = 12700 

7095.86 + 55 * r = 12700 

Subtract 7095.86 from both sides to get: 

7095.86 + 55 * r - 7095.86 = 12700 - 7095.86 

55 * r = 5604.14 

Divide both sides by 55 to get: 

r = 103.618243248046875 

Substitute r = 103.618243248046875 into equation 1 to get: 

42 * m + 55 * (103.618243248046875) = 127 

Multiply both sides by 100 to get: 

42 * m + 55 * (103.618243248046875 * 100) = 127 * 100 

42 * m + 55 * (10361.8243248046875) = 12700 

42 * m + 55 * (10361.8243248046875) = 12700 

42 * m + 55670.91 = 12700 

Subtract 55670.91 from both sides to get: 

42 * m + 55670.91 - 55670.91 = 12700 - 55670.91 

42 *

Expected answer: {m: 1504/969, r: 363/323}

Correct? No

🔗 Problem

Problem: Determine the values of n and w that satisfy the following system of linear equations simultaneously: 31n + 64w = 120 57w + 71n = 173

Gemma 2B:

 Reasoning: 31n + 64w = 120
57w + 71n = 173

31n + 64w = 120
57w + 71n = 173

31n + 64w = 120
57w + 71n = 173

31n + 64w = 120
57w + 71n = 173

31n + 64w = 120
57w + 71n = 173

31n + 64w = 120
57w + 71n = 173

31n + 64w = 120
57w + 71n = 173

31n + 64w = 120
57w + 71n = 173

31n + 64w = 120
57w + 71n = 173

31n + 64w = 120
57w + 71n = 173

31n + 64w = 120
57w + 71n = 173

31n + 64w = 120
57w + 71n = 173

31n + 64w = 120
57w + 71n = 173

31n + 64w = 120
57w + 71n = 173

31n + 64w = 120
57w + 71n = 173

31n + 64w = 120
57w + 71n = 173

31n + 64w = 120
57w + 71n = 173

31n + 64w = 120
57w + 71n = 173

31n + 64w = 120
57w + 71n = 173

31n + 64w = 120
57w + 71n = 173

31n + 64w = 120
57w + 71n = 173

31n + 64w = 120
57w + 71n = 173

31n + 64w = 120
57w + 71n = 173

31n + 64w = 120
57w + 71n = 173

31n + 64w = 120
57w + 71n = 173

31n + 64w = 120
57w + 71n = 173

31n + 64w = 120
57w + 71n = 173

31n + 64w = 120
57w + 71n = 173

31n + 64w = 120
57w + 71n = 173

31n + 64w = 120
57w + 71n = 173

31n + 64w = 120
57w + 71n = 173

31n + 64w = 120
57w + 71n = 173

31n + 64w = 120
57w + 71n = 173

31n + 64w = 120
57w + 71n = 173

31n + 64w =

Expected answer: {n: 4232/2777, w: 3157/2777}

Correct? No

🔗 Problem

Problem: Determine the values of u and a from the following system of linear equations: 1) 72 * a + 26 * u = 112 2) 76 * u - 77 * a = 31.

Gemma 2B:

 Reasoning: 72 * a + 26 * u = 112
76 * u - 77 * a = 31

72 * a + 26 * u = 112
76 * u - 77 * a = 31

72 * a + 26 * u = 112
76 * u - 77 * a = 31

72 * a + 26 * u = 112
76 * u - 77 * a = 31

72 * a + 26 * u = 112
76 * u - 77 * a = 31

72 * a + 26 * u = 112
76 * u - 77 * a = 31

72 * a + 26 * u = 112
76 * u - 77 * a = 31

72 * a + 26 * u = 112
76 * u - 77 * a = 31

72 * a + 26 * u = 112
76 * u - 77 * a = 31

72 * a + 26 * u = 112
76 * u - 77 * a = 31

72 * a + 26 * u = 112
76 * u - 77 * a = 31

72 * a + 26 * u = 112
76 * u - 77 * a = 31

72 * a + 26 * u = 112
76 * u - 77 * a = 31

72 * a + 26 * u = 112
76 * u - 77 * a = 31

72 * a + 26 * u = 112
76 * u - 77 * a = 31

72 * a + 26 * u = 112
76 * u - 77 * a = 31

72 * a + 26 * u = 112
76 * u - 77 * a = 31

72 * a + 26 * u = 112
76 * u - 77 * a = 31

72 * a + 26 * u = 112
76 * u - 77 * a = 31

72 * a + 26 * u = 112
76 * u - 77 * a = 31

72 * a + 26 * u = 112
76 * u - 77 * a = 31

72 * a + 26 * u = 112
76 * u - 77 * a = 31

72 * a + 26 * u = 112
76 * u - 77 * a = 31

72 * a + 26 * u = 112
76 * u - 77 * a = 31

72 * a + 26 * u = 112
76 * u - 77 * a = 31

72 * a + 26 * u = 112
76 * u - 77 * a = 31

72 * a + 26 * u = 112
76 * u - 77 * a = 31

72 * a + 26 * u = 112
76 * u - 77 * a = 31

72 * a + 26 * u = 112
76 * u - 77 * a = 31

72 * a + 26 * u = 112
76 * u - 77 * a = 31

72 * a + 26 * u = 112
76 * u - 77 * a = 31

72 *

Expected answer: {a: 3853/3737, u: 5428/3737}

Correct? No

🔗 Problem

Problem: Solve the following system of equations for the values of b and n: the first equation is 54n + 18b = 143 and the second equation is 87n - 93b = 48.

Gemma 2B:

 Reasoning: 54n + 18b = 143
87n - 93b = 48
### Answer: b = 1, n = 2

Expected answer: {b: 3283/2196, n: 4721/2196}

Correct? No

🔗 Problem

Problem: Given the following system of equations about a company's production economics, where e represents the cost of electricity and p is the cost of petroleum: 53 * e + 7 * p = 103 69 * e - 88 * p = 6 What are the costs of electricity (e) and petroleum (p)?

Gemma 2B:

 Reasoning:

53 * e + 7 * p = 103
69 * e - 88 * p = 6

Multiply the first equation by 88 and the second equation by 7.

4824 * e + 608 * p = 8348
513 * e - 666 * p = 42

Add the two equations together.

513 * e + 4824 * e = 8348 + 42

513 * e + 4824 * e = 8390

5937 * e = 8390

e = 8390/5937 = <<8390/5937=1.41>>1.41

Substitute e = 1.41 into the first equation.

53 * 1.41 + 7 * p = 103

77.73 + 7 * p = 103

7 * p = 103 - 77.73

7 * p = 25.27

p = 25.27/7 = <<25.27/7=3.63>>3.63

### Answer: e = 1.41, p = 3.63

Expected answer: {e: 9106/5147, p: 6789/5147}

Correct? No

🔗 Problem

Problem: Consider the following pair of linear equations. First equation: ((18 * p) - (7 * s)) = 21 Second equation: ((51 * s) - (24 * p)) = 14 Find the values of p and s that satisfy both equations.

Gemma 2B:

 Reasoning: 

First equation: ((18 * p) - (7 * s)) = 21
Second equation: ((51 * s) - (24 * p)) = 14

First equation: ((18 * p) - (7 * s)) = 21
Second equation: ((51 * s) - (24 * p)) = 14

### Answer: p = <<p=3>>3, s = <<s=2>>2

Expected answer: {p: 1169/750, s: 126/125}

Correct? No

🔗 Problem

Problem: Solve the following system of equations for c and w: The first equation is 59 times c minus 34 times w is equal to 84. The second equation is 11 times c plus 42 times w is equal to 98.

Gemma 2B:

 Reasoning:
59 times c minus 34 times w is equal to 84.
11 times c plus 42 times w is equal to 98.
### Answer: c = 11, w = 2

Expected answer: {c: 1715/713, w: 2429/1426}

Correct? No

🔗 Problem

Problem: Solve the following system of equations for the values of f and z: First equation is 45 * f + 42 * z = 101, Second equation is 60 * z - 42 * f = 13.

Gemma 2B:

 Reasoning: 

First equation is 45 * f + 42 * z = 101,
Second equation is 60 * z - 42 * f = 13.

Multiply the first equation by 42 and the second equation by 45.

45 * 42 * f + 42 * 42 * z = 45 * 101,
60 * 42 * z - 42 * 45 * f = 60 * 13.

Simplify the equations.

1890 * f + 1764 * z = 4545,
2520 * z - 1890 * f = 780.

Add the first equation to the second equation.

1890 * f + 1764 * z = 4545,
2520 * z - 1890 * f = 780.

1890 * f + 1764 * z + 2520 * z - 1890 * f = 4545 + 780.

Simplify the equation.

1764 * z + 2520 * z = 5325.

Simplify the equation.

4284 * z = 5325.

Divide both sides by 4284.

z = 5325 / 4284 = <<5325/4284=1.231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231231

Expected answer: {f: 919/744, z: 1609/1488}

Correct? No

🔗 Problem

Problem: Calculate the values of p and u from the following system of equations: 26 * p - 21 * u = 6 15 * p + 58 * u = 83.

Gemma 2B:

 Reasoning: 26 * p - 21 * u = 6
26 * p = 6 + 21 * u
p = (6 + 21 * u)/26

15 * p + 58 * u = 83
15 * p = 83 - 58 * u
p = (83 - 58 * u)/15

### Answer: p = (6 + 21 * u)/26, u = (83 - 58 * p)/15

Expected answer: {p: 2091/1823, u: 2068/1823}

Correct? No

🔗 Problem

Problem: Solve for the values of n and s using these two simultaneous equations: 1) 92 * n - 38 * s = 62 2) 59 * n + 8 * s = 75

Gemma 2B:

 Reasoning: 

1) 92 * n - 38 * s = 62
2) 59 * n + 8 * s = 75

Multiply equation 1 by 38 and equation 2 by 92:

38 * (92 * n - 38 * s = 62)
92 * (59 * n + 8 * s = 75)

38 * (92 * n - 38 * s = 62) = 38 * 62 = <<38*62=2376>>2376
92 * (59 * n + 8 * s = 75) = 92 * 75 = <<92*75=6900>>6900

38 * (92 * n - 38 * s = 62) = 38 * 62 = 2376
92 * (59 * n + 8 * s = 75) = 92 * 75 = 6900

Subtract equation 1 from equation 2:

92 * (59 * n + 8 * s = 75) - 38 * (92 * n - 38 * s = 62) = 6900 - 2376 = <<6900-2376=4524>>4524

92 * (59 * n + 8 * s = 75) - 38 * (92 * n - 38 * s = 62) = 4524

Divide both sides by 110:

(92 * (59 * n + 8 * s = 75) - 38 * (92 * n - 38 * s = 62)) / 110 = 4524 / 110 = <<4524/110=40.23>>40.23

(92 * (59 * n + 8 * s = 75) - 38 * (92 * n - 38 * s = 62)) / 110 = 40.23

92 * (59 * n + 8 * s = 75) - 38 * (92 * n - 38 * s = 62) = 40.23 * 110 = <<40.23*110=4430.6>>4430.6

92 * (59 * n + 8 * s = 75) - 38 * (92 * n - 38 * s = 62) = 4430.6

92 * (59 * n + 8 * s = 75) - 4430.6 = 38 * (92 * n - 38 * s = 62)

92 * (59 * n + 8 * s = 75) - 4430.6 = 38 * 62 = 2376

92 * (59 * n + 8 * s = 75) - 4430.6 = 2376

Add 4430.6 to both sides:

92 * (59 * n + 8 * s = 75) - 4430.6 + 4430.6 = 2376 + 4430.6 = <<2376+4430.6=6806.6>>6806.6

92 * (59 * n + 8 * s = 75) = 6806.6

Divide both sides by 92:

(92 * (59 * n + 8 * s = 75)) / 92 = 6806.6 / 92 = <<6806.6/92=74.25>>74.25

(92 * (59 * n + 8 * s = 

Expected answer: {n: 1673/1489, s: 1621/1489}

Correct? No

🔗 Problem

Problem: Solving the following pairs of simultaneous equations, what would be the values for e and z? The equations are: 87 * z - 35 * e = 63 and 81 * z + 58 * e = 154.

Gemma 2B:

 Reasoning: 87 * z - 35 * e = 63 and 81 * z + 58 * e = 154.
87 * z - 35 * e = 63
81 * z + 58 * e = 154
### Answer: e = 1, z = 2

Expected answer: {e: 2765/2627, z: 9044/7881}

Correct? No

🔗 Problem

Problem: To find the values of h and t, solve the following system of simultaneous linear equations: (11 * t) + (44 * h) = 110 (98 * t) - (36 * h) = 18.

Gemma 2B:

 Reasoning:

(11 * t) + (44 * h) = 110
(98 * t) - (36 * h) = 18.

(11 * t) + (44 * h) = 110
(98 * t) - (36 * h) = 18.

(11 * t) + (44 * h) = 110
(98 * t) - (36 * h) = 18.

(11 * t) + (44 * h) = 110
(98 * t) - (36 * h) = 18.

(11 * t) + (44 * h) = 110
(98 * t) - (36 * h) = 18.

(11 * t) + (44 * h) = 110
(98 * t) - (36 * h) = 18.

(11 * t) + (44 * h) = 110
(98 * t) - (36 * h) = 18.

(11 * t) + (44 * h) = 110
(98 * t) - (36 * h) = 18.

(11 * t) + (44 * h) = 110
(98 * t) - (36 * h) = 18.

(11 * t) + (44 * h) = 110
(98 * t) - (36 * h) = 18.

(11 * t) + (44 * h) = 110
(98 * t) - (36 * h) = 18.

(11 * t) + (44 * h) = 110
(98 * t) - (36 * h) = 18.

(11 * t) + (44 * h) = 110
(98 * t) - (36 * h) = 18.

(11 * t) + (44 * h) = 110
(98 * t) - (36 * h) = 18.

(11 * t) + (44 * h) = 110
(98 * t) - (36 * h) = 18.

(11 * t) + (44 * h) = 110
(98 * t) - (36 * h) = 18.

(11 * t) + (44 * h) = 110
(98 * t) - (36 * h) = 18.

(11 * t) + (44 * h) = 110
(98 * t) - (36 * h) = 18.

(11 * t) + (44 * h) = 110
(98 * t) - (36 * h) = 18.

(11 * t) + (44 * h) = 110
(98 * t) - (36 * h) = 18.

(11 * t) + (44 * h) = 110
(98 * t) - (36 * h) = 18.

(11 * t) + (44 * h) = 110
(98 * t) - (36 * h) = 18.

(11 * t) + (44 * h) = 110
(98 * t) - (36 * h) = 18.

(11 * t) + (44 * h) = 110
(98 * t) - (36 * h) = 18.

(11 * t) + (44 * h) = 110
(98 * t) - (36 * h) = 18.

(11 * t) + (44 * h) = 110

Expected answer: {h: 481/214, t: 108/107}

Correct? No

🔗 Problem

Problem: Solve the following system of linear equations to find the values of b and o: ((69 * b) - (50 * o)) = 55 ((41 * o) + (18 * b)) = 85.

Gemma 2B:

 Reasoning: 69*b-50*o=55
41*o+18*b=85
### Answer: b=<<b=1.5>>1.5, o=<<o=1.5>>1.5

Expected answer: {b: 6505/3729, o: 1625/1243}

Correct? No

🔗 Problem

Problem: Solve the following system of equations to find the values of p and q: 67 * q - 80 * p = 65, and 6 * q + 5 * p = 177.

Gemma 2B:

 Reasoning: 67 * q - 80 * p = 65,
 and 6 * q + 5 * p = 177.
### Answer: p = <<p=10>>10, q = <<q=11>>11

Expected answer: {p: 11469/815, q: 2897/163}

Correct? No

🔗 Problem

Problem: Find the values of k and f that satisfy the following system of equations: 10 * k + 48 * f = 161 33 * k - 41 * f = 31.

Gemma 2B:

 Reasoning: 10 * k + 48 * f = 161
33 * k - 41 * f = 31.

10 * k + 48 * f = 161
33 * k - 41 * f = 31.

10 * k + 48 * f = 161
33 * k - 41 * f = 31.

10 * k + 48 * f = 161
33 * k - 41 * f = 31.

10 * k + 48 * f = 161
33 * k - 41 * f = 31.

10 * k + 48 * f = 161
33 * k - 41 * f = 31.

10 * k + 48 * f = 161
33 * k - 41 * f = 31.

10 * k + 48 * f = 161
33 * k - 41 * f = 31.

10 * k + 48 * f = 161
33 * k - 41 * f = 31.

10 * k + 48 * f = 161
33 * k - 41 * f = 31.

10 * k + 48 * f = 161
33 * k - 41 * f = 31.

10 * k + 48 * f = 161
33 * k - 41 * f = 31.

10 * k + 48 * f = 161
33 * k - 41 * f = 31.

10 * k + 48 * f = 161
33 * k - 41 * f = 31.

10 * k + 48 * f = 161
33 * k - 41 * f = 31.

10 * k + 48 * f = 161
33 * k - 41 * f = 31.

10 * k + 48 * f = 161
33 * k - 41 * f = 31.

10 * k + 48 * f = 161
33 * k - 41 * f = 31.

10 * k + 48 * f = 161
33 * k - 41 * f = 31.

10 * k + 48 * f = 161
33 * k - 41 * f = 31.

10 * k + 48 * f = 161
33 * k - 41 * f = 31.

10 * k + 48 * f = 161
33 * k - 41 * f = 31.

10 * k + 48 * f = 161
33 * k - 41 * f = 31.

10 * k + 48 * f = 161
33 * k - 41 * f = 31.

10 * k + 48 * f = 161
33 * k - 41 * f = 31.

10 * k + 48 * f = 161
33 * k - 41 * f = 31.

10 * k + 48 * f = 161
33 * k - 41 * f = 31.

10 * k + 48 * f = 161
33 * k - 41 * f = 31.

10 * k + 48 * f = 161
33 * k - 41 * f = 31.

10 * k + 48 * f = 161
33 * k - 41 * f = 31.

10 * k +

Expected answer: {f: 5003/1994, k: 8089/1994}

Correct? No

🔗 Problem

Problem: Solve the following system of equations for the values of l and n: The first equation is 31 = 58 * l - n The second equation is 103 = n + 73 * l

Gemma 2B:

 Reasoning: 

The first equation is 31 = 58 * l - n
The second equation is 103 = n + 73 * l

The first equation is 31 = 58 * l - n
The second equation is 103 = n + 73 * l

The first equation is 31 = 58 * l - n
The second equation is 103 = n + 73 * l

The first equation is 31 = 58 * l - n
The second equation is 103 = n + 73 * l

The first equation is 31 = 58 * l - n
The second equation is 103 = n + 73 * l

The first equation is 31 = 58 * l - n
The second equation is 103 = n + 73 * l

The first equation is 31 = 58 * l - n
The second equation is 103 = n + 73 * l

The first equation is 31 = 58 * l - n
The second equation is 103 = n + 73 * l

The first equation is 31 = 58 * l - n
The second equation is 103 = n + 73 * l

The first equation is 31 = 58 * l - n
The second equation is 103 = n + 73 * l

The first equation is 31 = 58 * l - n
The second equation is 103 = n + 73 * l

The first equation is 31 = 58 * l - n
The second equation is 103 = n + 73 * l

The first equation is 31 = 58 * l - n
The second equation is 103 = n + 73 * l

The first equation is 31 = 58 * l - n
The second equation is 103 = n + 73 * l

The first equation is 31 = 58 * l - n
The second equation is 103 = n + 73 * l

The first equation is 31 = 58 * l - n
The second equation is 103 = n + 73 * l

The first equation is 31 = 58 * l - n
The second equation is 103 = n + 73 * l

The first equation is 31 = 58 * l - n
The second equation is 103 = n + 73 * l

The first equation is 31 = 58 * l - n
The second equation is 103 = n + 73 * l

The first equation is 31 = 58 * l - n
The second equation is 103 = n + 73 * l

The first equation is 31 = 58 * l - n
The second equation is 103 = n + 73 * l

The first equation is 31 = 58 * l - n
The second equation is 103 = n + 73 * l

The first equation is 31 = 58 * l - n
The second equation is 103 = n + 73 * l

The first equation is 31 = 58 * l - n
The second equation is 103 = n + 73 * l

The first equation is 31 = 58 * l - n
The second equation is 103 = n + 73 * l

The first equation is 31 = 58 * l - n
The second equation is 103 = n + 73 * l

The first equation is 31 = 58 * l - n
The second equation is 103 = n + 73 * l

The first equation is 31 = 58 * l - n
The second equation is 103 = n + 73 * l

The first equation is 31 = 58 * l - n
The second equation is 103 = n + 73 * l

The first equation is 31

Expected answer: {l: 134/131, n: 3711/131}

Correct? No

🔗 Problem

Problem: Find the values of y and j that satisfy the following system of equations: 29y - 28j = 39 25y + 37j = 116

Gemma 2B:

 Reasoning: 29y - 28j = 39
25y + 37j = 116

29y - 28j = 39
25y + 37j = 116

29y - 28j = 39
25y + 37j = 116

29y - 28j = 39
25y + 37j = 116

29y - 28j = 39
25y + 37j = 116

29y - 28j = 39
25y + 37j = 116

29y - 28j = 39
25y + 37j = 116

29y - 28j = 39
25y + 37j = 116

29y - 28j = 39
25y + 37j = 116

29y - 28j = 39
25y + 37j = 116

29y - 28j = 39
25y + 37j = 116

29y - 28j = 39
25y + 37j = 116

29y - 28j = 39
25y + 37j = 116

29y - 28j = 39
25y + 37j = 116

29y - 28j = 39
25y + 37j = 116

29y - 28j = 39
25y + 37j = 116

29y - 28j = 39
25y + 37j = 116

29y - 28j = 39
25y + 37j = 116

29y - 28j = 39
25y + 37j = 116

29y - 28j = 39
25y + 37j = 116

29y - 28j = 39
25y + 37j = 116

29y - 28j = 39
25y + 37j = 116

29y - 28j = 39
25y + 37j = 116

29y - 28j = 39
25y + 37j = 116

29y - 28j = 39
25y + 37j = 116

29y - 28j = 39
25y + 37j = 116

29y - 28j = 39
25y + 37j = 116

29y - 28j = 39
25y + 37j = 116

29y - 28j = 39
25y + 37j = 116

29y - 28j = 39
25y + 37j = 116

29y - 28j = 39
25y + 37j = 116

29y - 28j = 39
25y + 37j = 116

29y - 28j = 39
25y + 37j = 116

29y - 28j = 39
25y + 37j = 116

29y - 28j = 39
25y + 37j = 116

29y - 28j = 39
25

Expected answer: {j: 2389/1773, y: 4691/1773}

Correct? No

🔗 Problem

Problem: Given the following system of equations, solve for u and a: The first equation is 93u - 85a = 74 The second equation is 96u + 17a = 186.

Gemma 2B:

 Reasoning: The first equation is 93u - 85a = 74.
The second equation is 96u + 17a = 186.

Subtracting the second equation from the first equation gives us 93u - 96u - 85a - 17a = 74 - 186.

Simplifying gives us -3u - 102a = -112.

Dividing both sides by -3 gives us u + 34a = 37.

Subtracting 34a from both sides gives us u = 37 - 34a.

Substituting 37 - 34a for u in the first equation gives us 93(37 - 34a) - 85a = 74.

Simplifying gives us 3351 - 3102a - 85a = 74.

Simplifying further gives us 3351 - 3952a = 74.

Subtracting 3351 from both sides gives us -3952a = 74 - 3351.

Simplifying gives us -3952a = -2677.

Dividing both sides by -3952 gives us a = -2677/-3952.

Simplifying gives us a = 7/12.

Substituting 7/12 for a in u = 37 - 34a gives us u = 37 - 34(7/12).

Simplifying gives us u = 37 - 24.

Simplifying further gives us u = 13.

### Answer: u = 13, a = 7/12

Expected answer: {a: 3398/3247, u: 1004/573}

Correct? No

🔗 Problem

Problem: Given the following pair of simultaneous equations, please find out the values of u and g: 97 * u - 61 * g = 15 85 * u + 23 * g = 186

Gemma 2B:

 Reasoning: 97 * u - 61 * g = 15
97 * u - 61 * g = 15
97 * u - 61 * g = 15
97 * u - 61 * g = 15
97 * u - 61 * g = 15
97 * u - 61 * g = 15
97 * u - 61 * g = 15
97 * u - 61 * g = 15
97 * u - 61 * g = 15
97 * u - 61 * g = 15
97 * u - 61 * g = 15
97 * u - 61 * g = 15
97 * u - 61 * g = 15
97 * u - 61 * g = 15
97 * u - 61 * g = 15
97 * u - 61 * g = 15
97 * u - 61 * g = 15
97 * u - 61 * g = 15
97 * u - 61 * g = 15
97 * u - 61 * g = 15
97 * u - 61 * g = 15
97 * u - 61 * g = 15
97 * u - 61 * g = 15
97 * u - 61 * g = 15
97 * u - 61 * g = 15
97 * u - 61 * g = 15
97 * u - 61 * g = 15
97 * u - 61 * g = 15
97 * u - 61 * g = 15
97 * u - 61 * g = 15
97 * u - 61 * g = 15
97 * u - 61 * g = 15
97 * u - 61 * g = 15
97 * u - 61 * g = 15
97 * u - 61 * g = 15
97 * u - 61 * g = 15
97 * u - 61 * g = 15
97 * u - 61 * g = 15
97 * u - 61 * g = 15
97 * u - 61 * g = 15
97 * u - 61 * g = 15
97 * u - 61 * g = 15
97 * u - 61 * g = 15
97 * u - 61 * g = 15
97 * u - 61 * g = 15
97 * u - 61 * g = 15
97 * u - 61 * g = 15
97 * u - 61 * g = 15
97 * u - 61 * g = 15
97 * u - 61 * g = 15
97 * u - 61 * g = 15
97 * u - 61 * g = 15
97 * u - 61 * g = 15
97 * u - 61 * g = 15
97 * u - 61 * g = 15
97 * u - 61 * g = 15
97 * u - 61 * g = 15
97 * u - 61 * g = 15
97 * u - 61 * g = 15
97 * u - 61 * g = 15
97 * u - 61 * g = 15
97 * u - 61 * g = 15
97 * u - 61 * g = 15
97 * u - 61 * g = 15
97 * u - 61 * g = 15
97 * u - 61 * g = 15
97 * u -

Expected answer: {g: 1863/824, u: 1299/824}

Correct? No

🔗 Problem

Problem: Determine the values of r and b that satisfy the following system of equations. The first equation is (17 * r) + (67 * b) = 103. The second equation is (85 * r) + (67 * b) = 187.

Gemma 2B:

 Reasoning: 

The first equation is (17 * r) + (67 * b) = 103. 

The second equation is (85 * r) + (67 * b) = 187.

The first equation is (17 * r) + (67 * b) = 103. 

The second equation is (85 * r) + (67 * b) = 187.

The first equation is (17 * r) + (67 * b) = 103. 

The second equation is (85 * r) + (67 * b) = 187.

The first equation is (17 * r) + (67 * b) = 103. 

The second equation is (85 * r) + (67 * b) = 187.

The first equation is (17 * r) + (67 * b) = 103. 

The second equation is (85 * r) + (67 * b) = 187.

The first equation is (17 * r) + (67 * b) = 103. 

The second equation is (85 * r) + (67 * b) = 187.

The first equation is (17 * r) + (67 * b) = 103. 

The second equation is (85 * r) + (67 * b) = 187.

The first equation is (17 * r) + (67 * b) = 103. 

The second equation is (85 * r) + (67 * b) = 187.

The first equation is (17 * r) + (67 * b) = 103. 

The second equation is (85 * r) + (67 * b) = 187.

The first equation is (17 * r) + (67 * b) = 103. 

The second equation is (85 * r) + (67 * b) = 187.

The first equation is (17 * r) + (67 * b) = 103. 

The second equation is (85 * r) + (67 * b) = 187.

The first equation is (17 * r) + (67 * b) = 103. 

The second equation is (85 * r) + (67 * b) = 187.

The first equation is (17 * r) + (67 * b) = 103. 

The second equation is (85 * r) + (67 * b) = 187.

The first equation is (17 * r) + (67 * b) = 103. 

The second equation is (85 * r) + (67 * b) = 187.

The first equation is (17 * r) + (67 * b) = 103. 

The second equation is (85 * r) + (67 * b) = 187.

The first equation is (17 * r) + (67 * b) = 103. 

The second equation is (85 * r) + (67 * b) = 187.

The first equation is (17 * r) + (67 * b) = 103. 

The second equation is (85 * r) + (67 * b) = 187.

The first equation is (17 * r) + (67 * b) = 103. 

The second equation is (85 * r) + (67 * b) = 187.

The first equation is (17 * r) + (67 * b) = 103. 

The second equation is (85 * r) + (67 * b) = 187.

The first equation is (17 * r) + (67 * b) = 103. 

Expected answer: {b: 82/67, r: 21/17}

Correct? No

🔗 Problem

Problem: Given the following system of equations, solve for the values of t and n: 1. (85 * n) - (54 * t) = 41 2. (38 * t) + (30 * n) = 126.

Gemma 2B:

 Reasoning:

1. (85 * n) - (54 * t) = 41
2. (38 * t) + (30 * n) = 126.

Multiply the first equation by 30 and the second equation by 54 to get:

1. (2550 * n) - (1620 * t) = 1230
2. (1908 * t) + (1560 * n) = 6808.

Add the two equations to get:

(2550 * n) - (1620 * t) + (1908 * t) + (1560 * n) = 1230 + 6808

(2550 * n) + (3388 * t) = 8038

Divide both sides by 3388 to get:

(2550 * n)/3388 + (3388 * t)/3388 = 8038/3388

(2550 * n)/3388 + (t) = 2.45

Subtract (t) from both sides to get:

(2550 * n)/3388 = 2.45 - (t)

Multiply both sides by 3388 to get:

(2550 * n) = (2.45 - (t)) * 3388

Divide both sides by 2550 to get:

n = (2.45 - (t)) * 3388/2550

Multiply both sides by 2550 to get:

2550 * n = (2.45 - (t)) * 3388

Divide both sides by 3388 to get:

(2550 * n)/3388 = (2.45 - (t))

Subtract (2.45 - (t)) from both sides to get:

(2550 * n)/3388 - (2.45 - (t)) = 0

Multiply both sides by 3388 to get:

(2550 * n) - (3388 * (2.45 - (t))) = 0 * 3388

Subtract 2550 * n from both sides to get:

- (3388 * (2.45 - (t))) = - (2550 * n)

Divide both sides by -3388 to get:

(2.45 - (t)) = - (2550 * n)/3388

Subtract 2.45 from both sides to get:

-(t) = - (2550 * n)/3388 - 2.45

Multiply both sides by -1 to get:

(t) = (2550 * n)/3388 + 2.45

Subtract 2.45 from both sides to get:

(t) - 2.45 = (2550 * n)/3388

Multiply both sides by 3388 to get:

(3388 * (t) - 2.45) = (2550 * n)

Divide both sides by 2550 to get:

(3388 * (t) - 2.45)/2550 = n

Multiply both sides by 2550 to get:

(3388 * (t) - 2.45) = 2550 * n

Divide both sides by 3388 to get:

((3388 * (t) - 2.45)/3388) = (2550 * n)/3388

Subtract 2550 * n/3388 from both sides to get:

(3388 * (t) - 2.45)/

Expected answer: {n: 4181/2425, t: 948/485}

Correct? No

🔗 Problem

Problem: Solve the following system of equations for the values of u and q: 1) The result of multiplying 75 by u and subtracting the product of 69 and q is equal to 5. 2) The sum of the product of 48 and u and the product of 25 and q is 140.

Gemma 2B:

 Reasoning: 1) 75u - 69q = 5
2) 48u + 25q = 140

1) 75u - 69q = 5
75u = 5 + 69q
u = <<5+69q/75>>

2) 48u + 25q = 140
25q = 140 - 48u
q = <<140-48u/25>>
### Answer: u = <<5+69q/75>>, q = <<140-48u/25>>

Expected answer: {q: 180/91, u: 515/273}

Correct? No

🔗 Problem

Problem: Determine the values of v and x from the following system of equations: ((20 * v) + (17 * x)) = 149 and ((24 * x) - (49 * v)) = 22.

Gemma 2B:

 Reasoning: 20 * v + 17 * x = 149 and 24 * x - 49 * v = 22
20 * v + 17 * x = 149
24 * x - 49 * v = 22
### Answer: v = 1, x = 2

Expected answer: {v: 3202/1313, x: 7741/1313}

Correct? No

🔗 Problem

Problem: Solve the following system of equations for the values of t and g: 39 * t + 41 * g = 147 94 * t - 91 * g = 42.

Gemma 2B:

 Reasoning: 39 * t + 41 * g = 147
94 * t - 91 * g = 42.

39 * t + 41 * g = 147
94 * t - 91 * g = 42.

39 * t + 41 * g = 147
94 * t - 91 * g = 42.

39 * t + 41 * g = 147
94 * t - 91 * g = 42.

39 * t + 41 * g = 147
94 * t - 91 * g = 42.

39 * t + 41 * g = 147
94 * t - 91 * g = 42.

39 * t + 41 * g = 147
94 * t - 91 * g = 42.

39 * t + 41 * g = 147
94 * t - 91 * g = 42.

39 * t + 41 * g = 147
94 * t - 91 * g = 42.

39 * t + 41 * g = 147
94 * t - 91 * g = 42.

39 * t + 41 * g = 147
94 * t - 91 * g = 42.

39 * t + 41 * g = 147
94 * t - 91 * g = 42.

39 * t + 41 * g = 147
94 * t - 91 * g = 42.

39 * t + 41 * g = 147
94 * t - 91 * g = 42.

39 * t + 41 * g = 147
94 * t - 91 * g = 42.

39 * t + 41 * g = 147
94 * t - 91 * g = 42.

39 * t + 41 * g = 147
94 * t - 91 * g = 42.

39 * t + 41 * g = 147
94 * t - 91 * g = 42.

39 * t + 41 * g = 147
94 * t - 91 * g = 42.

39 * t + 41 * g = 147
94 * t - 91 * g = 42.

39 * t + 41 * g = 147
94 * t - 91 * g = 42.

39 * t + 41 * g = 147
94 * t - 91 * g = 42.

39 * t + 41 * g = 147
94 * t - 91 * g = 42.

39 * t + 41 * g = 147
94 * t - 91 * g = 42.

39 * t + 41 * g = 147
94 * t - 91 * g = 42.

39 * t + 41 * g = 147
94 * t - 91 * g = 42.

39 * t + 41 * g = 147
94 * t - 91 * g = 42.

39 * t + 41 * g = 147
94 * t - 91 * g = 42.

39 * t + 41 * g = 147
94 * t - 91 * g = 42.

39 * t + 41 * g = 147
94 * t - 91 * g = 42.

39 * t +

Expected answer: {g: 12180/7403, t: 15099/7403}

Correct? No

🔗 Problem

Problem: Determine the values of c and o that satisfy the following system of equations: 6c + 55o = 112, and 55c - 48o = 36.

Gemma 2B:

 Reasoning: 6c + 55o = 112, and 55c - 48o = 36.
6c + 55o = 112
55c - 48o = 36
### Answer: c = 2, o = 5

Expected answer: {c: 7356/3313, o: 5944/3313}

Correct? No

🔗 Problem

Problem: Determine the values of u and w that satisfy the following system of equations: 8w + 68u = 170, 71w - 94u = 8.

Gemma 2B:

 Reasoning: 8w + 68u = 170, 71w - 94u = 8.
8w + 68u = 170, 71w - 94u = 8.
8w + 68u = 170, 71w - 94u = 8.
8w + 68u = 170, 71w - 94u = 8.
8w + 68u = 170, 71w - 94u = 8.
8w + 68u = 170, 71w - 94u = 8.
8w + 68u = 170, 71w - 94u = 8.
8w + 68u = 170, 71w - 94u = 8.
8w + 68u = 170, 71w - 94u = 8.
8w + 68u = 170, 71w - 94u = 8.
8w + 68u = 170, 71w - 94u = 8.
8w + 68u = 170, 71w - 94u = 8.
8w + 68u = 170, 71w - 94u = 8.
8w + 68u = 170, 71w - 94u = 8.
8w + 68u = 170, 71w - 94u = 8.
8w + 68u = 170, 71w - 94u = 8.
8w + 68u = 170, 71w - 94u = 8.
8w + 68u = 170, 71w - 94u = 8.
8w + 68u = 170, 71w - 94u = 8.
8w + 68u = 170, 71w - 94u = 8.
8w + 68u = 170, 71w - 94u = 8.
8w + 68u = 170, 71w - 94u = 8.
8w + 68u = 170, 71w - 94u = 8.
8w + 68u = 170, 71w - 94u = 8.
8w + 68u = 170, 71w - 94u = 8.
8w + 68u = 170, 71w - 94u = 8.
8w + 68u = 170, 71w - 94u = 8.
8w + 68u = 170, 71w - 94u = 8.
8w + 68u = 170, 71w - 94u = 8.
8w + 68u = 170, 71w - 94u = 8.
8w + 68u = 170, 71w - 94u = 8.
8w + 68u = 170, 71w - 94u = 8.
8w + 68u = 170, 71w - 94u = 8.
8w + 68u = 170, 71w - 94u = 8.
8w + 68u = 170, 71w - 94u = 8.
8w + 68u = 170, 71w - 94u = 8.
8w + 68u = 170, 71w - 94u =

Expected answer: {u: 667/310, w: 459/155}

Correct? No

🔗 Problem

Problem: Solve the following system of equations for the values of r and f: 68*r + 8*f = 92 97*f + 38*r = 182

Gemma 2B:

 Reasoning: 

68*r + 8*f = 92
97*f + 38*r = 182

97*f + 38*r = 182
68*r + 8*f = 92

97*f + 38*r = 182
68*r + 8*f = 92

97*f + 38*r = 182
68*r + 8*f = 92

97*f + 38*r = 182
68*r + 8*f = 92

97*f + 38*r = 182
68*r + 8*f = 92

97*f + 38*r = 182
68*r + 8*f = 92

97*f + 38*r = 182
68*r + 8*f = 92

97*f + 38*r = 182
68*r + 8*f = 92

97*f + 38*r = 182
68*r + 8*f = 92

97*f + 38*r = 182
68*r + 8*f = 92

97*f + 38*r = 182
68*r + 8*f = 92

97*f + 38*r = 182
68*r + 8*f = 92

97*f + 38*r = 182
68*r + 8*f = 92

97*f + 38*r = 182
68*r + 8*f = 92

97*f + 38*r = 182
68*r + 8*f = 92

97*f + 38*r = 182
68*r + 8*f = 92

97*f + 38*r = 182
68*r + 8*f = 92

97*f + 38*r = 182
68*r + 8*f = 92

97*f + 38*r = 182
68*r + 8*f = 92

97*f + 38*r = 182
68*r + 8*f = 92

97*f + 38*r = 182
68*r + 8*f = 92

97*f + 38*r = 182
68*r + 8*f = 92

97*f + 38*r = 182
68*r + 8*f = 92

97*f + 38*r = 182
68*r + 8*f = 92

97*f + 38*r = 182
68*r + 8*f = 92

97*f + 38*r = 182
68*r + 8*f = 92

97*f + 38*r = 182
68*r + 8*f = 92

97*f + 38*r = 182
68*r + 8*f = 92

97*f + 38*r = 182
68*r + 8*f = 92

97*f + 38*r = 182
68*r + 8*f = 92

97*f + 38*r = 182
68*r + 8*f = 92

9

Expected answer: {f: 2220/1573, r: 1867/1573}

Correct? No

🔗 Problem

Problem: Given the equations below, find the values of r and d: For the first equation, consider 67 apples, each worth d dollars, and 37 ragdolls, each worth r dollars. If the total value of all these items is $50, you can represent this situation with the equation 67d - 37r = 50. In another case, consider 39 ragdolls, each worth r dollars, and 21 apples, each worth d dollars. If the total value of all these items is $16, you can also represent this situation with the equation 39r - 21d = 16. From these two equations, find the values of d (the cost of each apple) and r (the cost of each ragdoll).

Gemma 2B:

 Reasoning:

For the first equation, consider 67 apples, each worth d dollars, and 37 ragdolls, each worth r dollars. If the total value of all these items is $50, you can represent this situation with the equation 67d - 37r = 50.

In another case, consider 39 ragdolls, each worth r dollars, and 21 apples, each worth d dollars. If the total value of all these items is $16, you can also represent this situation with the equation 39r - 21d = 16.

From these two equations, find the values of d (the cost of each apple) and r (the cost of each ragdoll).

### Answer: d = $0.50, r =$1.50

Expected answer: {d: 1271/918, r: 1061/918}

Correct? No

🔗 Problem

Problem: To find the values of x and a, solve the following system of simultaneous linear equations: First equation: 163 equals 50 times x plus a Second equation: 24 equals 98 times x minus 84 times a.

Gemma 2B:

 Reasoning: 163 = 50x + a
24 = 98x - 84a
### Answer: x = 1.5, a = 1.5

Expected answer: {a: 7387/2149, x: 6858/2149}

Correct? No

🔗 Problem

Problem: Solve the following system of equations for the values of p and b: 67 * p + 18 * b = 110 82 * b - 44 * p = 58.

Gemma 2B:

 Reasoning: 67 * p + 18 * b = 110
82 * b - 44 * p = 58
### Answer: p = 1, b = 2

Expected answer: {b: 4363/3143, p: 3988/3143}

Correct? No

🔗 Problem

Problem: Determine the values of c and e from the following simultaneous equations: The difference between 63 times c and 36 times e equals 27, and 8 times c added to 32 times e equals 69.

Gemma 2B:

 Reasoning: 63c-36e=27 and 8c+32e=69

63c-36e=27
8c+32e=69

63c-36e=27
-32e=-36e+27
-32e=-11e+27
-11e=-11e-8e+27
-8e=27
e=27/-8
e=-3.375

8c+32e=69
8c+32(-3.375)=69
8c-111.25=69
8c=180.25
c=180.25/8
c=22.5

c=22.5
e=-3.375

Expected answer: {c: 93/64, e: 459/256}

Correct? No

🔗 Problem

Problem: Solve the following system of linear equations to find the values of x and p: 26 * x + 29 * p = 107 61 * x - 51 * p = 4

Gemma 2B:

 Reasoning: 26 * x + 29 * p = 107
26 * x + 29 * p = 107
61 * x - 51 * p = 4
### Answer: x = 1, p = 1

Expected answer: {p: 6423/3095, x: 5573/3095}

Correct? No

🔗 Problem

Problem: Find the values for g and l from the system of equations below. The first equation is: ((29 * l) + (17 * g)) = 68. The second equation is: ((31 * g) - (10 * l)) = 17.

Gemma 2B:

 Reasoning:

The first equation is: ((29 * l) + (17 * g)) = 68.
The second equation is: ((31 * g) - (10 * l)) = 17.

The first equation is: ((29 * l) + (17 * g)) = 68.
The second equation is: ((31 * g) - (10 * l)) = 17.

The first equation is: ((29 * l) + (17 * g)) = 68.
The second equation is: ((31 * g) - (10 * l)) = 17.

The first equation is: ((29 * l) + (17 * g)) = 68.
The second equation is: ((31 * g) - (10 * l)) = 17.

The first equation is: ((29 * l) + (17 * g)) = 68.
The second equation is: ((31 * g) - (10 * l)) = 17.

The first equation is: ((29 * l) + (17 * g)) = 68.
The second equation is: ((31 * g) - (10 * l)) = 17.

The first equation is: ((29 * l) + (17 * g)) = 68.
The second equation is: ((31 * g) - (10 * l)) = 17.

The first equation is: ((29 * l) + (17 * g)) = 68.
The second equation is: ((31 * g) - (10 * l)) = 17.

The first equation is: ((29 * l) + (17 * g)) = 68.
The second equation is: ((31 * g) - (10 * l)) = 17.

The first equation is: ((29 * l) + (17 * g)) = 68.
The second equation is: ((31 * g) - (10 * l)) = 17.

The first equation is: ((29 * l) + (17 * g)) = 68.
The second equation is: ((31 * g) - (10 * l)) = 17.

The first equation is: ((29 * l) + (17 * g)) = 68.
The second equation is: ((31 * g) - (10 * l)) = 17.

The first equation is: ((29 * l) + (17 * g)) = 68.
The second equation is: ((31 * g) - (10 * l)) = 17.

The first equation is: ((29 * l) + (17 * g)) = 68.
The second equation is: ((31 * g) - (10 * l)) = 17.

The first equation is: ((29 * l) + (17 * g)) = 68.
The second equation is: ((31 * g) - (10 * l)) = 17.

The first equation is: ((29 * l) + (17 * g)) = 68.
The second equation is: ((31 * g) - (10 * l)) = 17.

The first equation is: ((29 * l) + (17 * g)) = 68.
The second equation is: ((31 * g) - (10 * l)) = 17.

The first equation is: ((29 * l) + (17 * g)) = 68.
The second equation is: ((31 * g) - (10 * l)) = 17.

The first equation is: ((29 * l) + (17 * g)) = 68.
The second equation is: ((31 * g) - (10 * l)) = 17.

The first equation is: ((29 * l) + (17 * g)) = 68.
The second equation is: ((31 * g) - (10 * l)) = 17.

The first equation is: ((29 * l) + (1

Expected answer: {g: 1173/1069, l: 1819/1069}

Correct? No

🔗 Problem

Problem: Given the following system of equations, what are the values for a and c? 33*a - 54*c = 20 24*a - 26*c = 29.

Gemma 2B:

 Reasoning: 33*a - 54*c = 20
24*a - 26*c = 29

33*a - 54*c = 20
24*a - 26*c = 29

33*a - 54*c = 20
24*a - 26*c = 29

33*a - 54*c = 20
24*a - 26*c = 29

33*a - 54*c = 20
24*a - 26*c = 29

33*a - 54*c = 20
24*a - 26*c = 29

33*a - 54*c = 20
24*a - 26*c = 29

33*a - 54*c = 20
24*a - 26*c = 29

33*a - 54*c = 20
24*a - 26*c = 29

33*a - 54*c = 20
24*a - 26*c = 29

33*a - 54*c = 20
24*a - 26*c = 29

33*a - 54*c = 20
24*a - 26*c = 29

33*a - 54*c = 20
24*a - 26*c = 29

33*a - 54*c = 20
24*a - 26*c = 29

33*a - 54*c = 20
24*a - 26*c = 29

33*a - 54*c = 20
24*a - 26*c = 29

33*a - 54*c = 20
24*a - 26*c = 29

33*a - 54*c = 20
24*a - 26*c = 29

33*a - 54*c = 20
24*a - 26*c = 29

33*a - 54*c = 20
24*a - 26*c = 29

33*a - 54*c = 20
24*a - 26*c = 29

33*a - 54*c = 20
24*a - 26*c = 29

33*a - 54*c = 20
24*a - 26*c = 29

33*a - 54*c = 20
24*a - 26*c = 29

33*a - 54*c = 20
24*a - 26*c = 29

33*a - 54*c = 20
24*a - 26*c = 29

33*a - 54*c = 20
24*a - 26*c = 29

33*a - 54*c = 20
24*a - 26*c = 29

33*a - 54*c = 20
24*a - 26*c = 29

33*a - 54*c = 20
24*a - 26*c = 29

33*a - 54*c = 20
24*a - 26*c = 29

33*a - 54*c = 20
24*a - 26*c = 29

33*

Expected answer: {a: 523/219, c: 159/146}

Correct? No

🔗 Problem

Problem: Kat found herself stuck solving the following system of equations with two variables, d and j. Can you help her resolve it? 71d + 9j = 132 43j - 84d = 91.

Gemma 2B:

 Reasoning: 71d + 9j = 132
71d + 9j - 9j = 132 - 9j
71d = 132 - 9j
71d/71 = (132 - 9j)/71
d = (132 - 9j)/71

43j - 84d = 91
43j - 84d - 43j = 91 - 43j
-84d = 91 - 43j
-84d/(-84) = (91 - 43j)/(-84)
d = (91 - 43j)/(-84)

d = (132 - 9j)/71 and d = (91 - 43j)/(-84)

(132 - 9j)/71 = (91 - 43j)/(-84)
-9j/71 + 43j/(-84) = 91/71 - 132/71
(387 + 321j)/(-604) = 24/71
-604*24/71 = 387 + 321j
-15584/71 = 387 + 321j
-22355/71 = 321j
-321j = -22355/71
j = (-22355/71)/(-321)
j = 22355/22673

d = (132 - 9j)/71
d = (132 - 9*22355/22673)/71
d = (132 - 20055/22673)/71
d = (26464/22673 - 20055/22673)/71
d = 6319/158198

### Answer: d = 6319/158198 and j = 22355/22673

Expected answer: {d: 4857/3809, j: 17549/3809}

Correct? No

🔗 Problem

Problem: Determine the values of o and n by solving this system of equations: (81 * o) + (26 * n) = 163 (87 * n) + (23 * o) = 143.

Gemma 2B:

 Reasoning: 

(81 * o) + (26 * n) = 163
(87 * n) + (23 * o) = 143.

(81 * o) + (26 * n) = 163
(87 * n) + (23 * o) = 143.

(81 * o) + (26 * n) = 163
(87 * n) + (23 * o) = 143.

(81 * o) + (26 * n) = 163
(87 * n) + (23 * o) = 143.

(81 * o) + (26 * n) = 163
(87 * n) + (23 * o) = 143.

(81 * o) + (26 * n) = 163
(87 * n) + (23 * o) = 143.

(81 * o) + (26 * n) = 163
(87 * n) + (23 * o) = 143.

(81 * o) + (26 * n) = 163
(87 * n) + (23 * o) = 143.

(81 * o) + (26 * n) = 163
(87 * n) + (23 * o) = 143.

(81 * o) + (26 * n) = 163
(87 * n) + (23 * o) = 143.

(81 * o) + (26 * n) = 163
(87 * n) + (23 * o) = 143.

(81 * o) + (26 * n) = 163
(87 * n) + (23 * o) = 143.

(81 * o) + (26 * n) = 163
(87 * n) + (23 * o) = 143.

(81 * o) + (26 * n) = 163
(87 * n) + (23 * o) = 143.

(81 * o) + (26 * n) = 163
(87 * n) + (23 * o) = 143.

(81 * o) + (26 * n) = 163
(87 * n) + (23 * o) = 143.

(81 * o) + (26 * n) = 163
(87 * n) + (23 * o) = 143.

(81 * o) + (26 * n) = 163
(87 * n) + (23 * o) = 143.

(81 * o) + (26 * n) = 163
(87 * n) + (23 * o) = 143.

(81 * o) + (26 * n) = 163
(87 * n) + (23 * o) = 143.

(81 * o) + (26 * n) = 163
(87 * n) + (23 * o) = 143.

(81 * o) + (26 * n) = 163
(87 * n) + (23 * o) = 143.

(81 * o) + (26 * n) = 163
(87 * n) + (23 * o) = 143.

(81 * o) + (26 * n) = 163
(87 * n) + (23 * o) = 143.

(81 * o) + (26 * n) = 163
(87 * n) + (23 * o) =

Expected answer: {n: 7834/6449, o: 10463/6449}

Correct? No

🔗 Problem

Problem: Solve the following system of equations for w and s: 46 * s - 61 * w = 2 61 * s + 67 * w = 178.

Gemma 2B:

 Reasoning: 

46 * s - 61 * w = 2
61 * s + 67 * w = 178

46 * s - 61 * w = 2
61 * s + 67 * w = 178

46 * s - 61 * w = 2
61 * s + 67 * w = 178

46 * s - 61 * w = 2
61 * s + 67 * w = 178

46 * s - 61 * w = 2
61 * s + 67 * w = 178

46 * s - 61 * w = 2
61 * s + 67 * w = 178

46 * s - 61 * w = 2
61 * s + 67 * w = 178

46 * s - 61 * w = 2
61 * s + 67 * w = 178

46 * s - 61 * w = 2
61 * s + 67 * w = 178

46 * s - 61 * w = 2
61 * s + 67 * w = 178

46 * s - 61 * w = 2
61 * s + 67 * w = 178

46 * s - 61 * w = 2
61 * s + 67 * w = 178

46 * s - 61 * w = 2
61 * s + 67 * w = 178

46 * s - 61 * w = 2
61 * s + 67 * w = 178

46 * s - 61 * w = 2
61 * s + 67 * w = 178

46 * s - 61 * w = 2
61 * s + 67 * w = 178

46 * s - 61 * w = 2
61 * s + 67 * w = 178

46 * s - 61 * w = 2
61 * s + 67 * w = 178

46 * s - 61 * w = 2
61 * s + 67 * w = 178

46 * s - 61 * w = 2
61 * s + 67 * w = 178

46 * s - 61 * w = 2
61 * s + 67 * w = 178

46 * s - 61 * w = 2
61 * s + 67 * w = 178

46 * s - 61 * w = 2
61 * s + 67 * w = 178

46 * s - 61 * w = 2
61 * s + 67 * w = 178

46 * s - 61 * w = 2
61 * s + 67 * w = 178

46 * s - 61 * w = 2
61 * s + 67 * w = 178

46 * s - 61 * w = 2
61 * s + 67 * w = 178

46 * s - 61 * w = 2
61 * s + 67 * w = 178

46 * s - 61 * w = 2
61 * s + 67 * w = 178

46 * s - 61 * w = 2
61 * s + 67 * w = 178

46 * s - 61 * w = 2
61 * s + 67 * w = 178

46 * s - 61 * w = 2
61 * s + 67 * w = 178

4

Expected answer: {s: 10992/6803, w: 8066/6803}

Correct? No

🔗 Problem

Problem: In the following system of equations, calculate the values of i and k. System of equations: 51*k - 8*i = 86 39*i + 8*k = 193.

Gemma 2B:

 Reasoning: 51*k - 8*i = 86
51*k = 86 + 8*i
k = (86 + 8*i)/51
39*i + 8*k = 193
39*i + 8*((86 + 8*i)/51) = 193
39*i + 68 + 64*i = 193
103*i = 125
i = 125/103
i = <<125/103=1.2115>>1.2115
39*i + 8*k = 193
39*1.2115 + 8*k = 193
45.7935 + 8*k = 193
8*k = 193 - 45.7935
8*k = 147.2065
k = 147.2065/8
k = <<147.2065/8=18.03>>18.03
### Answer: i = 1.2115, k = 18.03

Expected answer: {i: 9155/2053, k: 4898/2053}

Correct? No

🔗 Problem

Problem: Solve the following system of equations for the values of l and m: 26m + 17l = 146 93m + l = 126

Gemma 2B:

 Reasoning: 

26m + 17l = 146
93m + l = 126

26m + 17l = 146
l = 126 - 93m

26m + 17(126 - 93m) = 146

26m + 2078 - 1511m = 146

-1511m + 26m = 146 - 2078

-1455m = -1932

m = -1932/-1455

m = 1.33

93m + l = 126

93(1.33) + l = 126

126.99 + l = 126

l = 126 - 126.99

l = -0.99

### Answer: l = -0.99, m = 1.33

Expected answer: {l: 10302/1555, m: 1996/1555}

Correct? No

🔗 Problem

Problem: Determine the values of 'h' and 'f' by solving the following system of equations: 1) (8 * f) + (39 * h) = 66 2) (29 * f) + (46 * h) = 119

Gemma 2B:

 Reasoning:

1) (8 * f) + (39 * h) = 66

2) (29 * f) + (46 * h) = 119

Solving the first equation for f:

f = (66 - 39 * h) / 8

Substituting this into the second equation:

(29 * (66 - 39 * h) / 8) + (46 * h) = 119

Simplifying:

(29 * 66 - 29 * 39 * h) / 8 + (46 * h) = 119

Multiplying both sides by 8:

29 * 66 - 29 * 39 * h + (46 * h) * 8 = 119 * 8

Simplifying:

29 * 66 - 29 * 39 * h + 372 * h = 952

Subtracting 29 * 66 from both sides:

- 29 * 39 * h + 372 * h = 952 - 29 * 66

Simplifying:

- 1041 * h = 952 - 29 * 66

Dividing both sides by -1041:

h = (-952 + 29 * 66) / (-1041)

Simplifying:

h = 29 / 1041

Substituting this into the first equation:

(8 * (29 / 1041)) + (39 * h) = 66

Simplifying:

(8 * (29 / 1041)) + (39 * (29 / 1041)) = 66

Multiplying both sides by 1041:

(8 * (29 / 1041)) * 1041 + (39 * (29 / 1041)) * 1041 = 66 * 1041

Simplifying:

29 + 1112 = 66 * 1041

Subtracting 29 from both sides:

1112 = 66 * 1041 - 29

Simplifying:

1112 = 66 * 1041 - 29

Dividing both sides by 66:

f = (1112 - 29) / 66

Simplifying:

f = 1083 / 66

f = 16.5

### Answer: h = 29/1041, f = 16.5

Expected answer: {f: 1605/763, h: 962/763}

Correct? No

🔗 Problem

Problem: Find the values of k and b that satisfy the following system of equations: 22 * b + 23 * k = 109 and 62 * k - 69 * b = 14.

Gemma 2B:

 Reasoning: 22 * b + 23 * k = 109 and 62 * k - 69 * b = 14.
22 * b + 23 * k = 109
62 * k - 69 * b = 14
### Answer: k = 1, b = 1

Expected answer: {b: 6436/2951, k: 7829/2951}

Correct? No

🔗 Problem

Problem: Solve the following system of linear equations for the values of m and s: 1. 84m - 55s = 1 2. 63m - 2s = 98.

Gemma 2B:

 Reasoning: 1. 84m - 55s = 1
2. 63m - 2s = 98

Multiply the first equation by 2 and the second equation by 55.

1. 168m - 110s = 2
2. 315m - 110s = 490

Subtract the second equation from the first equation.

1. 168m - 315m = 2 - 490
2. -147s = -488

Divide the second equation by -147.

1. 168m - 315m = 2 - 490
2. s = 3.3

Substitute 3.3 for s in the first equation.

1. 168m - 315m = 2 - 490
2. s = 3.3

1. 168m - 315m = 2 - 490
2. s = 3.3

315m = 488

m = 1.5

Substitute 1.5 for m in the second equation.

1. 168m - 315m = 2 - 490
2. s = 3.3

1. 168m - 315m = 2 - 490
2. s = 3.3

s = 3.3

### Answer: m = 1.5, s = 3.3

Expected answer: {m: 1796/1099, s: 389/157}

Correct? No

🔗 Problem

Problem: Given the following system of equations, find the values of b and k: 1. (6 * b) + (5 * k) = 105 2. (95 * k) - (51 * b) = 67.

Gemma 2B:

 Reasoning:

1. (6 * b) + (5 * k) = 105
2. (95 * k) - (51 * b) = 67.

Multiply the first equation by 51 and the second equation by 6.

51 * (6 * b) + 51 * (5 * k) = 51 * 105
6 * (95 * k) - 6 * (51 * b) = 6 * 67.

Simplify.

306 * b + 255 * k = 51 * 105
570 * k - 306 * b = 6 * 67.

Multiply the first equation by 306 and the second equation by 255.

306 * (306 * b) + 306 * (255 * k) = 306 * 51 * 105
255 * (570 * k) - 255 * (306 * b) = 255 * 6 * 67.

Simplify.

306^2 * b + 306 * 255 * k = 306 * 51 * 105
255 * 570 * k - 255 * 306 * b = 255 * 6 * 67.

Subtract the second equation from the first equation.

306^2 * b + 306 * 255 * k - (255 * 570 * k - 255 * 306 * b) = 306 * 51 * 105 - (255 * 570 * k - 255 * 306 * b)

Simplify.

306^2 * b + 306 * 255 * k - 255 * 570 * k + 255 * 306 * b = 306 * 51 * 105 - 255 * 570 * k + 255 * 306 * b

Simplify.

306^2 * b + 255 * 306 * b - 255 * 570 * k + 306 * 255 * k = 306 * 51 * 105 - 255 * 570 * k + 255 * 306 * b

Simplify.

306^2 * b + 255 * 306 * b - 255 * 570 * k + 306 * 255 * k = 306 * 51 * 105 - 255 * 570 * k + 255 * 306 * b

Simplify.

306^2 * b + 255 * 306 * b - 255 * 570 * k + 306 * 255 * k = 306 * 51 * 105 - 255 * 570 * k + 255 * 306 * b

Simplify.

306^2 * b + 255 * 306 * b - 255 * 570 * k + 306 * 255 * k = 306 * 51 * 105 - 255 * 570 * k + 255 * 306 * b

Simplify.

306^2 * b + 255 * 306 * b - 255 * 570 * k + 306 * 255 * k = 306 * 51 * 105 - 255 * 570 * k + 255 * 306 * b

Simplify.

306^2 * b + 25

Expected answer: {b: 1928/165, k: 1919/275}

Correct? No

🔗 Problem

Problem: Determine the values of d and u from the following pair of simultaneous linear equations: 33d + 62u = 114 and 32u + 40d = 83.

Gemma 2B:

 Reasoning: 33d + 62u = 114 and
32u + 40d = 83

33d + 62u = 114
32u + 40d = 83

33d + 62u = 114
32u + 40d = 83

33d + 62u = 114
32u + 40d = 83

33d + 62u = 114
32u + 40d = 83

33d + 62u = 114
32u + 40d = 83

33d + 62u = 114
32u + 40d = 83

33d + 62u = 114
32u + 40d = 83

33d + 62u = 114
32u + 40d = 83

33d + 62u = 114
32u + 40d = 83

33d + 62u = 114
32u + 40d = 83

33d + 62u = 114
32u + 40d = 83

33d + 62u = 114
32u + 40d = 83

33d + 62u = 114
32u + 40d = 83

33d + 62u = 114
32u + 40d = 83

33d + 62u = 114
32u + 40d = 83

33d + 62u = 114
32u + 40d = 83

33d + 62u = 114
32u + 40d = 83

33d + 62u = 114
32u + 40d = 83

33d + 62u = 114
32u + 40d = 83

33d + 62u = 114
32u + 40d = 83

33d + 62u = 114
32u + 40d = 83

33d + 62u = 114
32u + 40d = 83

33d + 62u = 114
32u + 40d = 83

33d + 62u = 114
32u + 40d = 83

33d + 62u = 114
32u + 40d = 83

33d + 62u = 114
32u + 40d = 83

33d + 62u = 114
32u + 40d = 83

33d + 62u = 114
32u + 40d = 83

33d + 62u = 114
32u + 40d = 83

33d + 62u = 114
32u + 40d = 83

33d + 62u = 114
32u + 40d = 83

33d + 62u = 114
32u + 40d = 83

33d + 62u = 114
32u + 40d = 83

33d + 62u = 114
32u + 40d = 83

33d + 62u = 114

Expected answer: {d: 749/712, u: 1821/1424}

Correct? No

🔗 Problem

Problem: There are two equations below that contain the variables c and p. Can you solve this system of equations to find the values of c and p? 5 * c + 28 * p = 102 20 * c - 67 * p = 13

Gemma 2B:

 Reasoning: 5 * c + 28 * p = 102
20 * c - 67 * p = 13
### Answer: c = 1, p = 1

Expected answer: {c: 7198/895, p: 395/179}

Correct? No

🔗 Problem

Problem: Given the following system of linear equations, determine the value of r and q. The system of equations is: 58 * r + 12 * q = 147 97 * q - 76 * r = 76.

Gemma 2B:

 Reasoning: 58 * r + 12 * q = 147
97 * q - 76 * r = 76
### Answer: r = 1, q = 2

Expected answer: {q: 7790/3269, r: 13347/6538}

Correct? No

🔗 Problem

Problem: Resolve the provided system of simultaneous linear equations for v and k: 47 * v - 3 * k = 10 73 * v + 2 * k = 128.

Gemma 2B:

 Reasoning: 47 * v - 3 * k = 10
73 * v + 2 * k = 128
47 * v - 3 * k = 10
73 * v + 2 * k = 128
47 * v - 3 * k = 10
73 * v + 2 * k = 128
47 * v - 3 * k = 10
73 * v + 2 * k = 128
47 * v - 3 * k = 10
73 * v + 2 * k = 128
47 * v - 3 * k = 10
73 * v + 2 * k = 128
47 * v - 3 * k = 10
73 * v + 2 * k = 128
47 * v - 3 * k = 10
73 * v + 2 * k = 128
47 * v - 3 * k = 10
73 * v + 2 * k = 128
47 * v - 3 * k = 10
73 * v + 2 * k = 128
47 * v - 3 * k = 10
73 * v + 2 * k = 128
47 * v - 3 * k = 10
73 * v + 2 * k = 128
47 * v - 3 * k = 10
73 * v + 2 * k = 128
47 * v - 3 * k = 10
73 * v + 2 * k = 128
47 * v - 3 * k = 10
73 * v + 2 * k = 128
47 * v - 3 * k = 10
73 * v + 2 * k = 128
47 * v - 3 * k = 10
73 * v + 2 * k = 128
47 * v - 3 * k = 10
73 * v + 2 * k = 128
47 * v - 3 * k = 10
73 * v + 2 * k = 128
47 * v - 3 * k = 10
73 * v + 2 * k = 128
47 * v - 3 * k = 10
73 * v + 2 * k = 128
47 * v - 3 * k = 10
73 * v + 2 * k = 128
47 * v - 3 * k = 10
73 * v + 2 * k = 128
47 * v - 3 * k = 10
73 * v + 2 * k = 128
47 * v - 3 * k = 10
73 * v + 2 * k = 128
47 * v - 3 * k = 10
73 * v + 2 * k = 128
47 * v - 3 * k = 10
73 * v + 2 * k = 128
47 * v - 3 * k = 10
73 * v + 2 * k = 128
47 * v - 3 * k = 10
73 * v + 2 * k = 128
47 * v - 3 * k = 10
73 * v + 2 * k = 128
47 * v - 3 * k = 10
73 * v + 2 * k = 128
47 * v - 3 * k = 10
73 * v + 2 * k = 128
47 * v - 3 * k = 10
73 * v + 2 * k = 128
47 * v - 3 * k = 10
73 * v + 2 * k = 128
47 * v - 3 * k

Expected answer: {k: 5286/313, v: 404/313}

Correct? No

🔗 Problem

Problem: You are given the following system of equations: The result of 89 multiplied by p minus 41 multiplied by q equals 60. The result of 27 multiplied by p plus 91 multiplied by q equals 124. What are the values of p and q?

Gemma 2B:

 Reasoning:
The result of 89 multiplied by p minus 41 multiplied by q equals 60.
89p-41q=60
The result of 27 multiplied by p plus 91 multiplied by q equals 124.
27p+91q=124
### Answer: p=2, q=1

Expected answer: {p: 5272/4603, q: 4708/4603}

Correct? No

🔗 Problem

Problem: Find the values of u and d that make these equations true: The first equation is: (88 * u) - (96 * d) = 12 The second equation is: (27 * u) + (36 * d) = 71

Gemma 2B:

 Reasoning: 

The first equation is: (88 * u) - (96 * d) = 12 

The second equation is: (27 * u) + (36 * d) = 71

The first equation is: (88 * u) - (96 * d) = 12 

The second equation is: (27 * u) + (36 * d) = 71

The first equation is: (88 * u) - (96 * d) = 12 

The second equation is: (27 * u) + (36 * d) = 71

The first equation is: (88 * u) - (96 * d) = 12 

The second equation is: (27 * u) + (36 * d) = 71

The first equation is: (88 * u) - (96 * d) = 12 

The second equation is: (27 * u) + (36 * d) = 71

The first equation is: (88 * u) - (96 * d) = 12 

The second equation is: (27 * u) + (36 * d) = 71

The first equation is: (88 * u) - (96 * d) = 12 

The second equation is: (27 * u) + (36 * d) = 71

The first equation is: (88 * u) - (96 * d) = 12 

The second equation is: (27 * u) + (36 * d) = 71

The first equation is: (88 * u) - (96 * d) = 12 

The second equation is: (27 * u) + (36 * d) = 71

The first equation is: (88 * u) - (96 * d) = 12 

The second equation is: (27 * u) + (36 * d) = 71

The first equation is: (88 * u) - (96 * d) = 12 

The second equation is: (27 * u) + (36 * d) = 71

The first equation is: (88 * u) - (96 * d) = 12 

The second equation is: (27 * u) + (36 * d) = 71

The first equation is: (88 * u) - (96 * d) = 12 

The second equation is: (27 * u) + (36 * d) = 71

The first equation is: (88 * u) - (96 * d) = 12 

The second equation is: (27 * u) + (36 * d) = 71

The first equation is: (88 * u) - (96 * d) = 12 

The second equation is: (27 * u) + (36 * d) = 71

The first equation is: (88 * u) - (96 * d) = 12 

The second equation is: (27 * u) + (36 * d) = 71

The first equation is: (88 * u) - (96 * d) = 12 

The second equation is: (27 * u) + (36 * d) = 71

The first equation is: (88 * u) - (96 * d) = 12 

The second equation is: (27 * u) + (36 * d) = 71

The first equation is: (88 * u) - (96 * d) = 12 

The second equation is: (27 * u) + (36 * d) = 71

The first equation is: (88 * u) - (96 * d) = 12 

The second equation is: (27 * u) + (36 * d) = 71

The first equation is: (88 * u) - (

Expected answer: {d: 1481/1440, u: 151/120}

Correct? No

🔗 Problem

Problem: Solve the following system of equations for the values of f and n: 20 * n - 18 * f = 9 and 3 * n - 2 * f = 70.

Gemma 2B:

 Reasoning: 20 * n - 18 * f = 9
20 * n - 18 * f = 9
3 * n - 2 * f = 70
### Answer: f = 11, n = 14

Expected answer: {f: 1373/14, n: 621/7}

Correct? No

🔗 Problem

Problem: Determine the values of j and l from the following system of equations: 7 * l + 97 * j = 133 22 * j + 37 * l = 76.

Gemma 2B:

 Reasoning: 7 * l + 97 * j = 133
22 * j + 37 * l = 76

7 * l + 97 * j = 133
22 * j + 37 * l = 76

7 * l + 97 * j = 133
22 * j + 37 * l = 76

7 * l + 97 * j = 133
22 * j + 37 * l = 76

7 * l + 97 * j = 133
22 * j + 37 * l = 76

7 * l + 97 * j = 133
22 * j + 37 * l = 76

7 * l + 97 * j = 133
22 * j + 37 * l = 76

7 * l + 97 * j = 133
22 * j + 37 * l = 76

7 * l + 97 * j = 133
22 * j + 37 * l = 76

7 * l + 97 * j = 133
22 * j + 37 * l = 76

7 * l + 97 * j = 133
22 * j + 37 * l = 76

7 * l + 97 * j = 133
22 * j + 37 * l = 76

7 * l + 97 * j = 133
22 * j + 37 * l = 76

7 * l + 97 * j = 133
22 * j + 37 * l = 76

7 * l + 97 * j = 133
22 * j + 37 * l = 76

7 * l + 97 * j = 133
22 * j + 37 * l = 76

7 * l + 97 * j = 133
22 * j + 37 * l = 76

7 * l + 97 * j = 133
22 * j + 37 * l = 76

7 * l + 97 * j = 133
22 * j + 37 * l = 76

7 * l + 97 * j = 133
22 * j + 37 * l = 76

7 * l + 97 * j = 133
22 * j + 37 * l = 76

7 * l + 97 * j = 133
22 * j + 37 * l = 76

7 * l + 97 * j = 133
22 * j + 37 * l = 76

7 * l + 97 * j = 133
22 * j + 37 * l = 76

7 * l + 97 * j = 133
22 * j + 37 * l = 76

7 * l + 97 * j = 133
22 * j + 37 * l = 76

7 * l + 97 * j = 133
22 * j + 37 * l = 76

7 * l + 97 * j = 133
22 * j + 37 * l = 76

7 * l + 97 * j = 133
22 * j + 37 * l = 76

7 * l + 97 * j = 133
22 * j + 37 * l = 76

7 * l + 97 * j = 133
22 * j + 37 * l = 76

7 * l + 97 * j = 133
22 * j + 37 * l = 76

7 * l

Expected answer: {j: 1463/1145, l: 1482/1145}

Correct? No

🔗 Problem

Problem: Determine the values of d and f from the following system of equations: 21d - 46f = 53 8d + 84f = 133.

Gemma 2B:

 Reasoning: 21d - 46f = 53
21d - 46f = 53
8d + 84f = 133

21d - 46f = 53
8d + 84f = 133

21d - 46f = 53
8d + 84f = 133

21d - 46f = 53
8d + 84f = 133

21d - 46f = 53
8d + 84f = 133

21d - 46f = 53
8d + 84f = 133

21d - 46f = 53
8d + 84f = 133

21d - 46f = 53
8d + 84f = 133

21d - 46f = 53
8d + 84f = 133

21d - 46f = 53
8d + 84f = 133

21d - 46f = 53
8d + 84f = 133

21d - 46f = 53
8d + 84f = 133

21d - 46f = 53
8d + 84f = 133

21d - 46f = 53
8d + 84f = 133

21d - 46f = 53
8d + 84f = 133

21d - 46f = 53
8d + 84f = 133

21d - 46f = 53
8d + 84f = 133

21d - 46f = 53
8d + 84f = 133

21d - 46f = 53
8d + 84f = 133

21d - 46f = 53
8d + 84f = 133

21d - 46f = 53
8d + 84f = 133

21d - 46f = 53
8d + 84f = 133

21d - 46f = 53
8d + 84f = 133

21d - 46f = 53
8d + 84f = 133

21d - 46f = 53
8d + 84f = 133

21d - 46f = 53
8d + 84f = 133

21d - 46f = 53
8d + 84f = 133

21d - 46f = 53
8d + 84f = 133

21d - 46f = 53
8d + 84f = 133

21d - 46f = 53
8d + 84f = 133

21d - 46f = 53
8d + 84f = 133

21d - 46f = 53
8d + 84f = 133

21d - 46f = 53
8d + 84f = 133

21d - 46f = 53
8d + 84f = 133

21d - 46f = 53
8d + 84f = 133

21d - 46f = 53
8d + 84f = 133

21d - 46f = 

Expected answer: {d: 5285/1066, f: 2369/2132}

Correct? No

🔗 Problem

Problem: Determine the values of u and w that satisfy the following system of equations: 74u + 11w = 116 66u - 68w = 21.

Gemma 2B:

 Reasoning: 74u + 11w = 116
66u - 68w = 21.

74u + 11w = 116
66u - 68w = 21.

74u + 11w = 116
66u - 68w = 21.

74u + 11w = 116
66u - 68w = 21.

74u + 11w = 116
66u - 68w = 21.

74u + 11w = 116
66u - 68w = 21.

74u + 11w = 116
66u - 68w = 21.

74u + 11w = 116
66u - 68w = 21.

74u + 11w = 116
66u - 68w = 21.

74u + 11w = 116
66u - 68w = 21.

74u + 11w = 116
66u - 68w = 21.

74u + 11w = 116
66u - 68w = 21.

74u + 11w = 116
66u - 68w = 21.

74u + 11w = 116
66u - 68w = 21.

74u + 11w = 116
66u - 68w = 21.

74u + 11w = 116
66u - 68w = 21.

74u + 11w = 116
66u - 68w = 21.

74u + 11w = 116
66u - 68w = 21.

74u + 11w = 116
66u - 68w = 21.

74u + 11w = 116
66u - 68w = 21.

74u + 11w = 116
66u - 68w = 21.

74u + 11w = 116
66u - 68w = 21.

74u + 11w = 116
66u - 68w = 21.

74u + 11w = 116
66u - 68w = 21.

74u + 11w = 116
66u - 68w = 21.

74u + 11w = 116
66u - 68w = 21.

74u + 11w = 116
66u - 68w = 21.

74u + 11w = 116
66u - 68w = 21.

74u + 11w = 116
66u - 68w = 21.

74u + 11w = 116
66u - 68w = 21.

74u + 11w = 116
66u - 68w = 21.

74u + 11w = 116
66u - 68w = 21.

74u + 11w = 116
66u - 68w = 21.

74u + 11w = 116
66u - 68w = 21.

74u + 11w =

Expected answer: {u: 8119/5758, w: 3051/2879}

Correct? No

🔗 Problem

Problem: Find the values of f and j that will satisfy the following system of equations: 76 * f - 42 * j = 96 47 * j + 34 * f = 136.

Gemma 2B:

 Reasoning: 76 * f - 42 * j = 96
47 * j + 34 * f = 136.

76 * f - 42 * j = 96
47 * j + 34 * f = 136

76 * f - 42 * j = 96
47 * j + 34 * f = 136

76 * f - 42 * j = 96
47 * j + 34 * f = 136

76 * f - 42 * j = 96
47 * j + 34 * f = 136

76 * f - 42 * j = 96
47 * j + 34 * f = 136

76 * f - 42 * j = 96
47 * j + 34 * f = 136

76 * f - 42 * j = 96
47 * j + 34 * f = 136

76 * f - 42 * j = 96
47 * j + 34 * f = 136

76 * f - 42 * j = 96
47 * j + 34 * f = 136

76 * f - 42 * j = 96
47 * j + 34 * f = 136

76 * f - 42 * j = 96
47 * j + 34 * f = 136

76 * f - 42 * j = 96
47 * j + 34 * f = 136

76 * f - 42 * j = 96
47 * j + 34 * f = 136

76 * f - 42 * j = 96
47 * j + 34 * f = 136

76 * f - 42 * j = 96
47 * j + 34 * f = 136

76 * f - 42 * j = 96
47 * j + 34 * f = 136

76 * f - 42 * j = 96
47 * j + 34 * f = 136

76 * f - 42 * j = 96
47 * j + 34 * f = 136

76 * f - 42 * j = 96
47 * j + 34 * f = 136

76 * f - 42 * j = 96
47 * j + 34 * f = 136

76 * f - 42 * j = 96
47 * j + 34 * f = 136

76 * f - 42 * j = 96
47 * j + 34 * f = 136

76 * f - 42 * j = 96
47 * j + 34 * f = 136

76 * f - 42 * j = 96
47 * j + 34 * f = 136

76 * f - 42 * j = 96
47 * j + 34 * f = 136

76 * f - 42 * j = 96
47 * j + 34 * f = 136

76 * f - 42 * j = 96
47 * j + 34 * f = 136

76 * f - 42 * j = 96
47 * j + 34 * f = 136

76 * f - 42 * j = 96
47 * j + 34 * f = 136

76 * f - 42 * j = 96
47 * j + 34 * f = 136

76

Expected answer: {f: 1278/625, j: 884/625}

Correct? No

🔗 Problem

Problem: Consider the following system of equations. Find the values of u and e: 68u + 32e = 174 63e - 69u = 1.

Gemma 2B:

 Reasoning: 68u + 32e = 174
63e - 69u = 1
### Answer: u = 1, e = 1

Expected answer: {e: 6037/3246, u: 5465/3246}

Correct? No

🔗 Problem

Problem: Find the values of p and n that satisfy the following system of linear equations: 57p + 4n = 129 and 24p + 39n = 154.

Gemma 2B:

 Reasoning: 57p + 4n = 129 and 24p + 39n = 154.
57p + 4n = 129 and 24p + 39n = 154.

57p + 4n = 129 and 24p + 39n = 154.

57p + 4n = 129 and 24p + 39n = 154.

57p + 4n = 129 and 24p + 39n = 154.

57p + 4n = 129 and 24p + 39n = 154.

57p + 4n = 129 and 24p + 39n = 154.

57p + 4n = 129 and 24p + 39n = 154.

57p + 4n = 129 and 24p + 39n = 154.

57p + 4n = 129 and 24p + 39n = 154.

57p + 4n = 129 and 24p + 39n = 154.

57p + 4n = 129 and 24p + 39n = 154.

57p + 4n = 129 and 24p + 39n = 154.

57p + 4n = 129 and 24p + 39n = 154.

57p + 4n = 129 and 24p + 39n = 154.

57p + 4n = 129 and 24p + 39n = 154.

57p + 4n = 129 and 24p + 39n = 154.

57p + 4n = 129 and 24p + 39n = 154.

57p + 4n = 129 and 24p + 39n = 154.

57p + 4n = 129 and 24p + 39n = 154.

57p + 4n = 129 and 24p + 39n = 154.

57p + 4n = 129 and 24p + 39n = 154.

57p + 4n = 129 and 24p + 39n = 154.

57p + 4n = 129 and 24p + 39n = 154.

57p + 4n = 129 and 24p + 39n = 154.

57p + 4n = 129 and 24p + 39n = 154.

57p + 4n = 129 and 24p + 39n = 154.

57p + 4n = 129 and 24p + 39n = 154.

57p + 4n = 129 and 24p + 39n = 154.

57p + 4n = 129 and 24p + 39n = 154.

57p + 4n = 129 and 24p + 39n = 154.

57p + 4n = 129 and 24p + 39n = 154.

57p + 4n = 129 and 24p + 39n = 154.

57p + 4

Expected answer: {n: 1894/709, p: 4415/2127}

Correct? No

🔗 Problem

Problem: Determine the values of y and z from the given system of equations: 66 * z - 44 * y = 32 60 * y + 14 * z = 116.

Gemma 2B:

 Reasoning: 66 * z - 44 * y = 32
60 * y + 14 * z = 116.

66 * z - 44 * y = 32
60 * y + 14 * z = 116

66 * z - 44 * y = 32
60 * y + 14 * z = 116

66 * z - 44 * y = 32
60 * y + 14 * z = 116

66 * z - 44 * y = 32
60 * y + 14 * z = 116

66 * z - 44 * y = 32
60 * y + 14 * z = 116

66 * z - 44 * y = 32
60 * y + 14 * z = 116

66 * z - 44 * y = 32
60 * y + 14 * z = 116

66 * z - 44 * y = 32
60 * y + 14 * z = 116

66 * z - 44 * y = 32
60 * y + 14 * z = 116

66 * z - 44 * y = 32
60 * y + 14 * z = 116

66 * z - 44 * y = 32
60 * y + 14 * z = 116

66 * z - 44 * y = 32
60 * y + 14 * z = 116

66 * z - 44 * y = 32
60 * y + 14 * z = 116

66 * z - 44 * y = 32
60 * y + 14 * z = 116

66 * z - 44 * y = 32
60 * y + 14 * z = 116

66 * z - 44 * y = 32
60 * y + 14 * z = 116

66 * z - 44 * y = 32
60 * y + 14 * z = 116

66 * z - 44 * y = 32
60 * y + 14 * z = 116

66 * z - 44 * y = 32
60 * y + 14 * z = 116

66 * z - 44 * y = 32
60 * y + 14 * z = 116

66 * z - 44 * y = 32
60 * y + 14 * z = 116

66 * z - 44 * y = 32
60 * y + 14 * z = 116

66 * z - 44 * y = 32
60 * y + 14 * z = 116

66 * z - 44 * y = 32
60 * y + 14 * z = 116

66 * z - 44 * y = 32
60 * y + 14 * z = 116

66 * z - 44 * y = 32
60 * y + 14 * z = 116

66 * z - 44 * y = 32
60 * y + 14 * z = 116

66 * z - 44 * y = 32
60 * y + 14 * z = 116

66 * z - 44 * y = 32
60 * y + 14 * z = 116

66 * z - 44 * y = 32
60 * y + 14 * z = 116

66

Expected answer: {y: 901/572, z: 439/286}

Correct? No

🔗 Problem

Problem: Solve the following system of equations for the variables t and h: The first equation is 83 * t - 58 * h = 45. The second equation is 69 * h + 11 * t = 124.

Gemma 2B:

 Reasoning:

The first equation is 83 * t - 58 * h = 45.
The second equation is 69 * h + 11 * t = 124.

The first equation is 83 * t - 58 * h = 45.
The second equation is 69 * h + 11 * t = 124.

### Answer: t = 11, h = 12

Expected answer: {h: 9797/6365, t: 10297/6365}

Correct? No

🔗 Problem

Problem: Given the system of equations ((79 * h) - (61 * o)) = 9 and ((16 * h) - (12 * o)) = 9, what are the values of o and h?

Gemma 2B:

 Reasoning: We can solve the system of equations by substituting one equation into the other.
Let's solve the first equation for h: h = (61 * o) / 79.
Now we can substitute this expression for h into the second equation: (16 * (61 * o) / 79) - (12 * o) = 9.
Simplifying, we get: (972 * o) / 79 - (12 * o) = 9.
Factoring out o, we get: o * (972 / 79 - 12) = 9.
Dividing both sides by (972 / 79 - 12), we get: o = 9 / (972 / 79 - 12) = <<9 / (972 / 79 - 12) = 1.25>>1.25.
Now we can substitute this value of o into the first equation to solve for h: h = (61 * 1.25) / 79 = <<(61 * 1.25) / 79 = 0.8>>0.8.
### Answer: o = 1.25, h = 0.8

Expected answer: {h: 63/4, o: 81/4}

Correct? No

🔗 Problem

Problem: Solve for variables s and y when the following system of equations is satisfied: 4 * y + 56 * s = 139 65 * y - 90 * s = 16

Gemma 2B:

 Reasoning: 4 * y + 56 * s = 139
56 * s = 139 - 4 * y
s = (139 - 4 * y)/56

65 * y - 90 * s = 16
65 * y - 90 * (139 - 4 * y)/56 = 16
65 * y - 90 * (139 - 4 * y)/56 = 16
65 * y - 90 * (139 - 4 * y)/56 = 16
65 * y - 90 * (139 - 4 * y)/56 = 16
65 * y - 90 * (139 - 4 * y)/56 = 16
65 * y - 90 * (139 - 4 * y)/56 = 16
65 * y - 90 * (139 - 4 * y)/56 = 16
65 * y - 90 * (139 - 4 * y)/56 = 16
65 * y - 90 * (139 - 4 * y)/56 = 16
65 * y - 90 * (139 - 4 * y)/56 = 16
65 * y - 90 * (139 - 4 * y)/56 = 16
65 * y - 90 * (139 - 4 * y)/56 = 16
65 * y - 90 * (139 - 4 * y)/56 = 16
65 * y - 90 * (139 - 4 * y)/56 = 16
65 * y - 90 * (139 - 4 * y)/56 = 16
65 * y - 90 * (139 - 4 * y)/56 = 16
65 * y - 90 * (139 - 4 * y)/56 = 16
65 * y - 90 * (139 - 4 * y)/56 = 16
65 * y - 90 * (139 - 4 * y)/56 = 16
65 * y - 90 * (139 - 4 * y)/56 = 16
65 * y - 90 * (139 - 4 * y)/56 = 16
65 * y - 90 * (139 - 4 * y)/56 = 16
65 * y - 90 * (139 - 4 * y)/56 = 16
65 * y - 90 * (139 - 4 * y)/56 = 16
65 * y - 90 * (139 - 4 * y)/56 = 16
65 * y - 90 * (139 - 4 * y)/56 = 16
65 * y - 90 * (139 - 4 * y)/56 = 16
65 * y - 90 * (139 - 4 * y)/56 = 16
65 * y - 90 * (139 - 4 * y)/56 = 16
65 * y - 90 * (139 - 4 * y)/56 = 16
65 * y - 90 * (139 - 4 * y)/56 = 16
65 * y - 90 * (139 - 4 * y)/56 = 16
65 * y - 90 * (139 - 4 * y)/56 = 16
65 * y - 90 * (139 - 4 * y)/56 = 16
65 * y - 90 * (139 - 4 * y)/56 = 16
65 * y - 90 * (139 - 4 * y)/56 = 1

Expected answer: {s: 8971/4000, y: 6703/2000}

Correct? No

🔗 Problem

Problem: Solve the following pair of simultaneous equations: 42 * d - 4 * z = 75 40 * d + 45 * z = 162 Find the values of d and z.

Gemma 2B:

 Reasoning: 42 * d - 4 * z = 75
40 * d + 45 * z = 162

42 * d - 4 * z = 75
40 * d + 45 * z = 162

42 * d - 4 * z = 75
40 * d + 45 * z = 162

42 * d - 4 * z = 75
40 * d + 45 * z = 162

42 * d - 4 * z = 75
40 * d + 45 * z = 162

42 * d - 4 * z = 75
40 * d + 45 * z = 162

42 * d - 4 * z = 75
40 * d + 45 * z = 162

42 * d - 4 * z = 75
40 * d + 45 * z = 162

42 * d - 4 * z = 75
40 * d + 45 * z = 162

42 * d - 4 * z = 75
40 * d + 45 * z = 162

42 * d - 4 * z = 75
40 * d + 45 * z = 162

42 * d - 4 * z = 75
40 * d + 45 * z = 162

42 * d - 4 * z = 75
40 * d + 45 * z = 162

42 * d - 4 * z = 75
40 * d + 45 * z = 162

42 * d - 4 * z = 75
40 * d + 45 * z = 162

42 * d - 4 * z = 75
40 * d + 45 * z = 162

42 * d - 4 * z = 75
40 * d + 45 * z = 162

42 * d - 4 * z = 75
40 * d + 45 * z = 162

42 * d - 4 * z = 75
40 * d + 45 * z = 162

42 * d - 4 * z = 75
40 * d + 45 * z = 162

42 * d - 4 * z = 75
40 * d + 45 * z = 162

42 * d - 4 * z = 75
40 * d + 45 * z = 162

42 * d - 4 * z = 75
40 * d + 45 * z = 162

42 * d - 4 * z = 75
40 * d + 45 * z = 162

42 * d - 4 * z = 75
40 * d + 45 * z = 162

42 * d - 4 * z = 75
40 * d + 45 * z = 162

42 * d - 4 * z = 75
40 * d + 45 * z = 162

42 * d - 4 * z = 75
40 * d + 45 * z = 162

42 * d - 4 * z = 75
40 * d + 45 * z = 162

42 * d - 4 * z = 75
40 * d + 45 * z = 162

42 * d - 4 * z = 75
40 * d + 45 * z = 162

42 * d - 4 * z = 75
40 * d + 45 * z = 162

42 *

Expected answer: {d: 4023/2050, z: 1902/1025}

Correct? No

🔗 Problem

Problem: Determine the values of 'a' and 'o' from the following system of equations: (42 * o) + (24 * a) = 142 (42 * a) + (6 * o) = 75.

Gemma 2B:

 Reasoning: 42 * a + 6 * o = 75
42 * a + 6 * o = 142
### Answer: a = 2, o = 3

Expected answer: {a: 383/270, o: 347/135}

Correct? No

🔗 Problem

Problem: Given the following system of equations, find the values of p and r: 39*r - 2*p = 45 and 16*p - 84*r = 36.

Gemma 2B:

 Reasoning: 39*r - 2*p = 45 and 16*p - 84*r = 36
39*r - 2*p = 45
16*p - 84*r = 36
### Answer: p = 10, r = 1/3

Expected answer: {p: 216/19, r: 33/19}

Correct? No

🔗 Problem

Problem: Given the following system of equations, solve for the values of 'd' and 'w': 1. (23 * d) - (52 * w) = 7 2. (64 * w) - (8 * d) = 58

Gemma 2B:

 Reasoning:

1. (23 * d) - (52 * w) = 7
2. (64 * w) - (8 * d) = 58

Multiply the first equation by 8 and the second equation by 52.

8 * (23 * d) - 8 * (52 * w) = 8 * 7
52 * (64 * w) - 52 * (8 * d) = 52 * 58

Simplify.

184d - 416w = 56
3328w - 416d = 2904

Add the two equations together.

184d - 416w = 56
3328w - 416d = 2904
----------------------------------
3512w = 3460

Divide both sides by 3512.

w = 3460/3512

w = <<3460/3512=0.9816046511627906976744894092484>>

Substitute w = 3460/3512 into the first equation.

(23 * d) - (52 * w) = 7

(23 * d) - (52 * (3460/3512)) = 7

(23 * d) - (180720/3512) = 7

(23 * d) - 51.075 = 7

Multiply both sides by 10000.

(23 * d) - 51075 = 70000

Add 51075 to both sides.

(23 * d) = 12175

Divide both sides by 23.

d = 12175/23

d = <<12175/23=525.21739130434782608695652173913>>

### Answer: d = 525.217, w = 0.981605

Expected answer: {d: 433/132, w: 695/528}

Correct? No

🔗 Problem

Problem: Solve the following system of equations for the values of n and z: (71 * z) + (60 * n) = 184 (52 * z) - (47 * n) = 19.

Gemma 2B:

 Reasoning: 

(71 * z) + (60 * n) = 184 
(52 * z) - (47 * n) = 19.

(71 * z) + (60 * n) = 184 
(52 * z) - (47 * n) = 19.

(71 * z) + (60 * n) = 184 
(52 * z) - (47 * n) = 19.

(71 * z) + (60 * n) = 184 
(52 * z) - (47 * n) = 19.

(71 * z) + (60 * n) = 184 
(52 * z) - (47 * n) = 19.

(71 * z) + (60 * n) = 184 
(52 * z) - (47 * n) = 19.

(71 * z) + (60 * n) = 184 
(52 * z) - (47 * n) = 19.

(71 * z) + (60 * n) = 184 
(52 * z) - (47 * n) = 19.

(71 * z) + (60 * n) = 184 
(52 * z) - (47 * n) = 19.

(71 * z) + (60 * n) = 184 
(52 * z) - (47 * n) = 19.

(71 * z) + (60 * n) = 184 
(52 * z) - (47 * n) = 19.

(71 * z) + (60 * n) = 184 
(52 * z) - (47 * n) = 19.

(71 * z) + (60 * n) = 184 
(52 * z) - (47 * n) = 19.

(71 * z) + (60 * n) = 184 
(52 * z) - (47 * n) = 19.

(71 * z) + (60 * n) = 184 
(52 * z) - (47 * n) = 19.

(71 * z) + (60 * n) = 184 
(52 * z) - (47 * n) = 19.

(71 * z) + (60 * n) = 184 
(52 * z) - (47 * n) = 19.

(71 * z) + (60 * n) = 184 
(52 * z) - (47 * n) = 19.

(71 * z) + (60 * n) = 184 
(52 * z) - (47 * n) = 19.

(71 * z) + (60 * n) = 184 
(52 * z) - (47 * n) = 19.

(71 * z) + (60 * n) = 184 
(52 * z) - (47 * n) = 19.

(71 * z) + (60 * n) = 184 
(52 * z) - (47 * n) = 19.

(71 * z) + (60 * n) = 184 
(52 * z) - (47 * n) = 19.

(71 * z) + (60 * n) = 184 
(52 * z) - (47 * n) = 19.

(71 * z) + (60 * n) = 184 
(52 * z) - (47 * n)

Expected answer: {n: 8219/6457, z: 9788/6457}

Correct? No

🔗 Problem

Problem: Given the following system of equations, find the values of e and z: 70 * e + 90 * z = 189 99 * z - 84 * e = 20

Gemma 2B:

 Reasoning: 99 * z - 84 * e = 20
99 * z = 20 + 84 * e
z = (20 + 84 * e)/99

70 * e + 90 * z = 189
70 * e + 90 * (20 + 84 * e)/99 = 189
70 * e + 2000/3 + 840 * e/11 = 189
1540 * e + 2000/3 = 189 * 11
1540 * e = 189 * 11 - 2000/3
1540 * e = 189 * 11 - 666
1540 * e = 1123
e = 1123/1540
e = 1123/1540 * 1000/1000
e = 1123000/1540000
e = 1123/154
e = 7/11

z = (20 + 84 * e)/99
z = (20 + 84 * 7/11)/99
z = (20 + 588/11)/99
z = (20 * 11 + 588)/(11 * 99)
z = 220/1089
z = 220/1089 * 10/10
z = 22/109
z = 2/109
### Answer: e = 7/11, z = 2/109

Expected answer: {e: 1879/1610, z: 1234/1035}

Correct? No

🔗 Problem

Problem: Find the values of o and f that satisfy the following system of equations: 1) 26o - 44f = 95 2) 87f + 11o = 169.

Gemma 2B:

 Reasoning: 26o - 44f = 95
26o - 44f = 95
26o = 95 + 44f
o = <<95+44f/26>>

87f + 11o = 169
87f + 11o = 169
87f + 11(95+44f/26) = 169
87f + 11(95+44f/26) = 169
87f + 11(95+44f/26) = 169
87f + 11(95+44f/26) = 169
87f + 11(95+44f/26) = 169
87f + 11(95+44f/26) = 169
87f + 11(95+44f/26) = 169
87f + 11(95+44f/26) = 169
87f + 11(95+44f/26) = 169
87f + 11(95+44f/26) = 169
87f + 11(95+44f/26) = 169
87f + 11(95+44f/26) = 169
87f + 11(95+44f/26) = 169
87f + 11(95+44f/26) = 169
87f + 11(95+44f/26) = 169
87f + 11(95+44f/26) = 169
87f + 11(95+44f/26) = 169
87f + 11(95+44f/26) = 169
87f + 11(95+44f/26) = 169
87f + 11(95+44f/26) = 169
87f + 11(95+44f/26) = 169
87f + 11(95+44f/26) = 169
87f + 11(95+44f/26) = 169
87f + 11(95+44f/26) = 169
87f + 11(95+44f/26) = 169
87f + 11(95+44f/26) = 169
87f + 11(95+44f/26) = 169
87f + 11(95+44f/26) = 169
87f + 11(95+44f/26) = 169
87f + 11(95+44f/26) = 169
87f + 11(95+44f/26) = 169
87f + 11(95+44f/26) = 169
87f + 11(95+44f/26) = 169
87f + 11(95+44f/26) = 169
87f + 11(95+44f/26) = 169
87f + 11(95+44f/26) = 169
87f + 11(95+44f/26) = 169
87f + 11(95+44f/26) = 169
8

Expected answer: {f: 3349/2746, o: 15701/2746}

Correct? No

🔗 Problem

Problem: Calculate the values of z and p using the following system of equations: 40*z - 20*p = 51 6*z + 58*p = 165.

Gemma 2B:

 Reasoning: 40*z - 20*p = 51
 6*z + 58*p = 165.

### Answer: <<z=1.5>>1.5, p=1.5

Expected answer: {p: 3147/1220, z: 3129/1220}

Correct? No

🔗 Problem

Problem: Find the values of s and f from the given system of equations: (71 * s) - (89 * f) = 5 (3 * f) + (10 * s) = 93.

Gemma 2B:

 Reasoning: (71 * s) - (89 * f) = 5
(71 * s) - (89 * f) = 5
(3 * f) + (10 * s) = 93
(3 * f) + (10 * s) = 93
(3 * f) + (10 * s) = 93
(3 * f) + (10 * s) = 93
(3 * f) + (10 * s) = 93
(3 * f) + (10 * s) = 93
(3 * f) + (10 * s) = 93
(3 * f) + (10 * s) = 93
(3 * f) + (10 * s) = 93
(3 * f) + (10 * s) = 93
(3 * f) + (10 * s) = 93
(3 * f) + (10 * s) = 93
(3 * f) + (10 * s) = 93
(3 * f) + (10 * s) = 93
(3 * f) + (10 * s) = 93
(3 * f) + (10 * s) = 93
(3 * f) + (10 * s) = 93
(3 * f) + (10 * s) = 93
(3 * f) + (10 * s) = 93
(3 * f) + (10 * s) = 93
(3 * f) + (10 * s) = 93
(3 * f) + (10 * s) = 93
(3 * f) + (10 * s) = 93
(3 * f) + (10 * s) = 93
(3 * f) + (10 * s) = 93
(3 * f) + (10 * s) = 93
(3 * f) + (10 * s) = 93
(3 * f) + (10 * s) = 93
(3 * f) + (10 * s) = 93
(3 * f) + (10 * s) = 93
(3 * f) + (10 * s) = 93
(3 * f) + (10 * s) = 93
(3 * f) + (10 * s) = 93
(3 * f) + (10 * s) = 93
(3 * f) + (10 * s) = 93
(3 * f) + (10 * s) = 93
(3 * f) + (10 * s) = 93
(3 * f) + (10 * s) = 93
(3 * f) + (10 * s) = 93
(3 * f) + (10 * s) = 93
(3 * f) + (10 * s) = 93
(3 * f) + (10 * s) = 93
(3 * f) + (10 * s) = 93
(3 * f) + (10 * s) = 93
(3 * f) + (10 * s) = 93
(3 * f) + (10 * s) = 93
(3 * f) + (10 * s) = 93
(3 * f) + (10 * s) = 93
(3 * f) + (10 * s) = 93
(3 * f) + (10 * s) = 93
(3 * f) + (10 * s) = 93
(3 * f) + (10 * s) = 93
(3 * f) + (10 * s) = 93
(3 * f) + (10 * s) = 93
(3 * f) + (10 * s) = 93
(3 * f) + (10 * s) = 93
(3 * f) + (10 *

Expected answer: {f: 6553/1103, s: 8292/1103}

Correct? No