🔗 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

CodeLlama 7B:

      To solve this system of equations, we can use substitution or elimination. Let's use substitution.

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

    We can solve for q by solving the first equation for s and then substituting that value into the second equation.

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

    Substituting s = 40/91q into the second equation, we get:

    2. (30 * (40/91q)) + (12 * q) = 121

    Simplifying, we get:

    2. 30/91q + 12q = 121

    Subtracting 12q from both sides, we get:

    2. 30/91q = 109

    Dividing both sides by 30/91, we get:

    2. q = 109/30

    Now that we have the value of q, we can substitute it into the first equation to solve for s.

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

    Substituting q = 109/30 into the first equation, we get:

    1. (40 * s) - (91 * (109/30)) = 37

    Simplifying, we get:

    1. 40s - 9109/30 = 37

    Dividing both sides by 9109/30, we get:

    1. s = 40/91

    Therefore, the values of q and s are q = 109/30 and s = 40/91.

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.

CodeLlama 7B:

      To solve this system of equations, we can first add the two equations to get:

    4 * b + 44 * m = 180
    79 * m - 6 * b = 48

    Adding the two equations, we get:

    4 * b + 79 * m = 228

    Subtracting 44 * m from both sides, we get:

    4 * b - 79 * m = 184

    Dividing both sides by 4, we get:

    b - 19.5 * m = 42

    Now, we can solve for b and m separately.

    For b, we have:

    b = 42 + 19.5 * m

    For m, we have:

    m = (b - 42) / 19.5

    Substituting the expression for b in terms of m, we get:

    m = (42 + 19.5 * m) / 19.5

    Simplifying, we get:

    m = 2

    Therefore, the values of b and m are b = 42 and m = 2.

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.

CodeLlama 7B:

      To solve this system of equations, we can first add the two equations to get:

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

    This simplifies to:

    69 * o + 46 * g = 169

    Now, we can divide both sides of the equation by 69 to get:

    o + g = 2.46

    Since we want to find the values of o and g, we can set up the equation:

    o + g = 2.46

    and solve for o and g separately.

    o = 2.46 - g

    Now, we can substitute this expression for o into the second equation:

    47 * (2.46 - g) + 29 * g = 141

    This simplifies to:

    47 * 2.46 - 47 * g + 29 * g = 141

    This simplifies to:

    47 * 2.46 = 116.42

    Now, we can divide both sides of the equation by 47 to get:

    2.46 = 116.42 / 47

    This simplifies to:

    g = 2.46 / 47

    Now, we can substitute this expression for g into the first equation:

    o + g = 2.46

    This simplifies to:

    o = 2.46 - g

    Now, we can substitute this expression for o into the first equation:

    2.46 - g + g = 2.46

    This simplifies to:

    o = 2.46

    Now, we have found the values of o and g:

    o = 2.46
    g = 2.46 / 47

    Therefore, the values of o and g are 2.46 and 0.52, respectively.

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.

CodeLlama 7B:

      To solve this system of equations, we need to find the values of v and o that satisfy both equations.

    First, let's solve the first equation for v:

    v = (21 + 6o) / 12

    Now, substitute this expression for v into the second equation:

    ((76 * (21 + 6o) / 12) - (45 * o)) = 50

    Expand and simplify:

    (172 + 42o) - 45o = 50

    Combine like terms:

    127o = 5

    Now, divide both sides by 127 to find o:

    o = 5 / 127

    Now that we have the value of o, we can substitute it into the first equation to find the value of v:

    v = (21 + 6o) / 12
    = (21 + 6(5/127)) / 12
    = (21 + 3) / 12
    = 15 / 12

    Therefore, the values of v and o are:

    v = 15/12
    o = 5/127

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.

CodeLlama 7B:

      To solve this system of equations, we can first solve the first equation for f:

    75 * f + 25 * g = 138

    Subtracting 25 * g from both sides gives us:

    50 * f = 138 - 25 * g

    Dividing both sides by 50 gives us:

    f = (138 - 25 * g) / 50

    Now, substitute this expression for f into the second equation:

    2 * (f) + 90 * g = 143

    Expanding and simplifying gives us:

    2 * ((138 - 25 * g) / 50) + 90 * g = 143

    Expanding and simplifying gives us:

    138 - 25 * g + 180 * g = 143

    Subtracting 180 * g from both sides gives us:

    -65 * g = 10

    Dividing both sides by -65 gives us:

    g = -10 / 65

    Now, substitute this expression for g into the first equation:

    75 * f + 25 * (-10 / 65) = 138

    Expanding and simplifying gives us:

    75 * f - 10 = 138

    Dividing both sides by 75 gives us:

    f = 138 / 75

    Therefore, the values of f and g are:

    f = 138 / 75
    g = -10 / 65

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.

CodeLlama 7B:

      To solve this system of equations, we can first solve the second equation for y:

    7 = 65n - 79y

    We can then substitute this expression for y into the first equation:

    194 = 4(65n - 79y) + 14n

    Now, we can solve for n:

    194 = 4(65n) + 14n - 79y

    Subtracting 4(65n) from both sides gives us:

    194 - 4(65n) = 14n - 79y

    Simplifying, we get:

    150n = 14n - 79y

    Subtracting 14n from both sides gives us:

    136n = -79y

    Dividing both sides by -79 gives us:

    n = -y/79

    Now, we can substitute this expression for n into the first equation:

    194 = 4(-y/79) + 14(-y/79)

    Simplifying, we get:

    194 = -y/79 + 14/79

    Adding 14/79 to both sides gives us:

    194 + 14/79 = -y/79

    Simplifying, we get:

    194 + 14/79 = -y/79 + 14/79

    Combining like terms, we get:

    194 + 14/79 = 0

    Subtracting 14/79 from both sides gives us:

    170/79 = -y/79

    Dividing both sides by -y/79 gives us:

    79 = -y

    Substituting this expression for y into the first equation, we get:

    194 = 4(-y) + 14(-y)

    Simplifying, we get:

    194 = -4y + 14y

    Adding 4y to both sides gives us:

    194 + 4y = 14y

    Subtracting 14y from both sides gives us:

    170 = 4y

    Dividing both sides by 4 gives us:

    40 = y

    Therefore, the value of y is 40.

    Now, we can substitute this expression for y into the second equation:

    7 = 65n - 79(40)

    Simplifying, we get:

    7 = 65n - 3240

    Dividing both sides by 65 gives us:

    n = 11.2

    Therefore, the value of n is 11.2.

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.

CodeLlama 7B:

      To find the values of l and g that satisfy these two equations, we can start by solving the first equation for g:

    146 = 28 * g + 26 * l

    Subtracting 26 * l from both sides gives us:

    28 * g = 146 - 26 * l

    Dividing both sides by 28 gives us:

    g = (146 - 26 * l) / 28

    Now, we can substitute this expression for g into the second equation:

    6 = 41 * l - 53 * (146 - 26 * l) / 28

    Simplifying this equation gives us:

    6 = 41 * l - 53 * g

    Subtracting 53 * g from both sides gives us:

    41 * l = 6 + 53 * g

    Dividing both sides by 41 gives us:

    l = (6 + 53 * g) / 41

    Now, we can substitute this expression for l into the first equation:

    146 = 28 * g + 26 * (6 + 53 * g) / 41

    Simplifying this equation gives us:

    146 = 28 * g + 26 * (6 + 53 * g) / 41

    Subtracting 26 * (6 + 53 * g) / 41 from both sides gives us:

    28 * g = 146 - 26 * (6 + 53 * g) / 41

    Dividing both sides by 28 gives us:

    g = (146 - 26 * (6 + 53 * g) / 41) / 28

    Now, we can substitute this expression for g into the second equation:

    6 = 41 * l - 53 * (146 - 26 * (6 + 53 * g) / 41) / 28

    Simplifying this equation gives us:

    6 = 41 * l - 53 * g

    Subtracting 53 * g from both sides gives us:

    41 * l = 6 + 53 * g

    Dividing both sides by 41 gives us:

    l = (6 + 53 * g) / 41

    Now, we have found the values of l and g that satisfy both equations. Substituting these values into the first equation gives us:

    146 = 28 * g + 26 * (6 + 53 * g) / 41

    Simplifying this equation gives us:

    146 = 28 * g + 26 * (6 + 53 * g) / 41

    Subtracting 26 * (6 + 53 * g) / 41 from both sides gives us:

    28 * g = 146 - 26 * (6 + 53 * g) / 41

    Dividing both sides by 28 gives us:

    g = (146 - 26 * (6 + 53 * g) / 41) / 28

    Now, we have found the values of l and g that satisfy both equations.

    ### Answer:

    l = (6 + 53 * g) / 41
    g = (146 - 26 * (6 + 53 * g) / 41) / 28

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.

CodeLlama 7B:

      To resolve this system of equations, we need to find the values of p and y that satisfy both equations.

    First, we can solve the first equation for p:

    p = (90 - 56y) / 20

    Now, substitute this expression for p into the second equation:

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

    Expand and simplify:

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

    890 - 56y + 7y = 98

    890 - 56y = 91

    56y = 890 - 91

    y = 890 / 56

    Now, we can find the value of p:

    p = (90 - 56y) / 20

    p = (90 - 890 / 56) / 20

    p = 10 / 20

    p = 0.5

    Therefore, the values of p and y that satisfy both equations are p = 0.5 and y = 890 / 56.

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.

CodeLlama 7B:

      To solve this system of equations, we need to follow these steps:

    1. Add the two equations:
    72*k - 22*d = 17 + 6*d + 69*k = 96
    2. Combine like terms:
    72*k - 22*d + 6*d + 69*k = 96 + 6*d
    3. Simplify:
    72*k - 84*d = 96 + 6*d
    4. Solve for d:
    d = (96 + 72*k) / 84
    5. Solve for k:
    k = (96 + 6*d) / 72

    Now we have the values of d and k:
    d = 3 and k = 4

    Therefore, the values of variables d and k are 3 and 4, respectively.

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

CodeLlama 7B:

      To solve this system of equations, we can first add the two equations to get:

    73 * h - 33 * d = 48
    10 * d + 14 * h = 91

    Adding the two equations, we get:

    83 * h = 134

    Dividing both sides by 83, we get:

    h = 15

    Now, we can substitute the value of h into the first equation to get:

    73 * 15 - 33 * d = 48

    Subtracting 33 * d from both sides, we get:

    49 * d = 11

    Dividing both sides by 49, we get:

    d = 2

    Now, we can substitute the value of d into the second equation to get:

    10 * 2 + 14 * 15 = 91

    Simplifying, we get:

    28 + 210 = 238

    Subtracting 210 from both sides, we get:

    28 = 138

    Dividing both sides by 28, we get:

    h = 15

    Therefore, the values of d and h are 2 and 15, respectively.

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

CodeLlama 7B:

      To solve this system of equations, we can first add the two equations to eliminate the variable e:

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

    Adding the two equations, we get:

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

    Adding the two equations, we get:

    73 * q = 159

    Dividing both sides by 73, we get:

    q = 21

    Now, we can substitute the value of q into one of the original equations to solve for e:

    1) 43 * 21 - 44 * e = 29

    Subtracting 44 * e from both sides, we get:

    43 * 21 - 44 * e = 29

    Subtracting 44 * e from both sides, we get:

    21 * 43 - 44 * e = 29

    Dividing both sides by 43, we get:

    21 - e = 29/43

    Subtracting 29/43 from both sides, we get:

    e = 21/43

    Therefore, the values of q and e are:

    q = 21
    e = 21/43

    So, the values of q and e are 21 and 21/43, respectively.

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))

CodeLlama 7B:

      To solve this system of equations, we can first solve the first equation for r:

    53 = ((89 * r) - (74 * a))

    We can solve for r by adding 74a to both sides:

    53 + 74a = (89 * r)

    Now, we can divide both sides by 89:

    (53 + 74a) / 89 = r

    Now, we can solve for r by multiplying both sides by 89:

    r = (53 + 74a) / 89

    Now, we can substitute the value of a from the second equation into the first equation:

    r = (53 + 74(37)) / 89

    Now, we can simplify the expression:

    r = (53 + 2,610) / 89

    Now, we can simplify the expression further:

    r = 30 / 89

    Now, we can simplify the expression further:

    r = 0.33

    Now, we can substitute the value of r into the first equation:

    a = (53 - 74(0.33)) / 37

    Now, we can simplify the expression:

    a = (53 - 24.95) / 37

    Now, we can simplify the expression further:

    a = 16 / 37

    Now, we can simplify the expression further:

    a = 4

    Therefore, the values of r and a are 0.33 and 4, respectively.

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.

CodeLlama 7B:

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

    1. The sum of the weights of 42 units of 'g' and 12 units of 'q' equals 169 kg.
    2. The weight of 42 units of 'g' is 169 kg - 12 units of 'q'.
    3. The weight of 12 units of 'q' is 169 kg - 42 units of 'g'.

    Now, let's substitute the value of 'g' into the second equation:

    1. The weight of 12 units of 'q' minus the weight of 50 units of 'g' results in 19 kg.
    2. The weight of 12 units of 'q' minus 50 units of 'g' is 19 kg.

    Now, let's solve for 'q':

    1. The weight of 12 units of 'q' is 169 kg - 42 units of 'g'.
    2. The weight of 12 units of 'q' is 169 kg - 42 units of 'g' - 19 kg.

    Now, let's solve for 'g':

    1. The weight of 42 units of 'g' is 169 kg - 12 units of 'q'.
    2. The weight of 42 units of 'g' is 169 kg - 12 units of 'q' - 19 kg.

    Now, let's solve for 'q':

    1. The weight of 12 units of 'q' is 169 kg - 42 units of 'g'.
    2. The weight of 12 units of 'q' is 169 kg - 42 units of 'g' - 19 kg.

    Now, let's solve for 'g':

    1. The weight of 42 units of 'g' is 169 kg - 12 units of 'q'.
    2. The weight of 42 units of 'g' is 169 kg - 12 units of 'q' - 19 kg.

    Now, let's solve for 'q':

    1. The weight of 12 units of 'q' is 169 kg - 42 units of 'g'.
    2. The weight of 12 units of 'q' is 169 kg - 42 units of 'g' - 19 kg.

    Now, let's solve for 'g':

    1. The weight of 42 units of 'g' is 169 kg - 12 units of 'q'.
    2. The weight of 42 units of 'g' is 169 kg - 12 units of 'q' - 19 kg.

    Now, let's solve for 'q':

    1. The weight of 12 units of 'q' is 169 kg - 42 units of 'g'.
    2. The weight of 12 units of 'q' is 169 kg - 42 units of 'g' - 19 kg.

    Now, let's solve for 'g':

    1. The weight of 42 units of 'g' is 169 kg - 12 units of 'q'.
    2. The weight of 42 units of 'g' is 169 kg - 12 units of 'q' - 19 kg.

    Now, let's solve for 'q':

    1. The weight of 12 units of 'q' is 169 kg - 42 units of 'g'.
    2. The weight of 12 units of 'q' is 169 kg - 42 units of 'g' - 19 kg.

    Now, let's solve for 'g':

    1. The weight of 42 units of 'g' is 169 kg - 12 units of 'q'.
    2. The weight of 42 units of 'g' is 169 kg - 12 units of 'q' - 19 kg.

    Now, let's solve for 'q':

    1. The weight of 12 units of 'q' is 169 kg - 42 units of 'g'.

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

CodeLlama 7B:

      To solve this system of equations, we can first add the two equations to eliminate the variable v:

    37 * s - 11 * v = 54
    82 * s - 62 * v = 41

    Adding the two equations, we get:

    119 * s = 95

    Now, we can divide both sides by 119 to solve for s:

    s = 95 / 119

    Now, we can substitute the value of s into one of the original equations to solve for v:

    37 * s - 11 * v = 54

    Substituting s = 95 / 119, we get:

    37 * (95 / 119) - 11 * v = 54

    Simplifying, we get:

    v = 54 / 11

    Therefore, the values of s and v are:

    s = 95 / 119
    v = 54 / 11

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.

CodeLlama 7B:

      To solve this system of equations, we need to follow these steps:

    1. Subtract the first equation from the second equation to eliminate the variable c:
    78 * z - 48 * c = 48
    41 * c + 65 * z = 151
    78 * z - 48 * c = 48
    41 * c + 65 * z - 48 * c = 151 - 48
    36 * z = 103
    z = 103 / 36
    z = 3
    2. Now, substitute the value of z back into the first equation to find the value of c:
    41 * c + 65 * 3 = 151
    141 * c = 151
    c = 151 / 141
    c = 3

    Therefore, the values for c and z are:
    c = 3
    z = 3

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?

CodeLlama 7B:

      To solve this system of equations, we can first add the two equations to eliminate the variable i:

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

    Adding the two equations, we get:

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

    Adding the two equations, we get:

    67c = 155

    Dividing both sides by 7, we get:

    c = 22

    Now, we can substitute the value of c into one of the original equations to solve for i:

    60c - 91i = 7

    Substituting c = 22, we get:

    60(22) - 91i = 7

    Simplifying, we get:

    1320 - 91i = 7

    Dividing both sides by 91, we get:

    14.07 - i = 7/91

    Dividing both sides by 14.07, we get:

    i = 5/14.07

    Therefore, the values of c and i are c = 22 and i = 5/14.07.

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

CodeLlama 7B:

      To solve this system of equations, we can first add the two equations to get:

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

    Adding the two equations, we get:

    117*v = 252

    Dividing both sides by 117, we get:

    v = 22

    Now, we can substitute the value of v into one of the original equations to solve for e:

    71*22 - 37*e = 69

    Subtracting 37*e from both sides, we get:

    71*22 - 37*e = 69

    Subtracting 37*e from both sides, we get:

    114*22 = 252

    Dividing both sides by 114, we get:

    e = 2

    Therefore, the values of e and v that satisfy the two simultaneous linear equations are e = 2 and v = 22.

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.

CodeLlama 7B:

      To solve this system of equations, we can first solve the first equation for 'v' and then substitute that value into the second equation to solve for 'd'.

    First, solve the first equation for 'v':

    25x + 69y = 113

    Now, solve for 'y' in the second equation:

    26x + 42y = 85

    Now, substitute the value of 'y' from the first equation into the second equation:

    26x + 42(25x + 69y) = 85

    Simplify the equation:

    26x + 1125x + 3269y = 85

    Combine like terms:

    3994x + 3269y = 85

    Now, solve for 'x' and 'y':

    3994x = 85 - 3269y

    x = 85 - 3269y / 3994

    y = (85 - 3994x) / 3269

    Now, we have the values of 'x' and 'y':

    x = 85 - 3269y / 3994
    y = (85 - 3994x) / 3269

    Therefore, the values of 'd' and 'v' are:

    d = y = (85 - 3994x) / 3269
    v = x = 85 - 3269y / 3994

    So, the values of 'd' and 'v' are:

    d = (85 - 3269y) / 3269
    v = (85 - 3994x) / 3994

    Note: These values are not the only solutions to the system of equations. There may be other solutions as well.

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

CodeLlama 7B:

      To solve these equations, we can first add the two equations together to get:

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

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

    This simplifies to:

    115 * z = 101

    Now, we can divide both sides by 115 to solve for z:

    z = 101 / 115

    Now, we can substitute this value of z into one of the original equations to solve for g:

    43 * z - 91 * g = 33

    Substituting z = 101 / 115, we get:

    43 * (101 / 115) - 91 * g = 33

    Simplifying, we get:

    43 - 91 * g = 33

    Now, we can divide both sides by -91 to solve for g:

    g = -43 / 91

    Now, we can substitute this value of g into one of the original equations to solve for z:

    72 * g - 3 * z = 68

    Substituting g = -43 / 91, we get:

    72 * (-43 / 91) - 3 * z = 68

    Simplifying, we get:

    -282 - 3 * z = 68

    Now, we can add 3 * z to both sides to get:

    -282 + 3 * z = 68 + 3 * z

    Now, we can simplify by combining like terms:

    -282 + 3 * z = 101

    Now, we can divide both sides by 3 to solve for z:

    -282 / 3 + z = 101 / 3

    Now, we can simplify by combining like terms:

    -92 + z = 34

    Now, we can subtract 34 from both sides to solve for z:

    -92 + z - 34 = 0

    Now, we can simplify by combining like terms:

    -126 = 0

    Now, we can divide both sides by -126 to solve for z:

    1 / -126 = 0

    Now, we can simplify by combining like terms:

    z = 0

    Therefore, the values of g and z are:

    g = -43 / 91
    z = 0

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.

CodeLlama 7B:

      To solve this system of equations, we can first add the two equations to get:

    50c + 12f = 92
    36c - 21f = 34

    Adding the two equations, we get:

    86c = 126

    Dividing both sides by 86, we get:

    c = 126/86

    c = 1.4

    Now, we can substitute the value of c into one of the original equations to solve for f. For example, we can substitute c = 1.4 into the first equation:

    50(1.4) + 12f = 92

    Simplifying, we get:

    68 + 12f = 92

    Subtracting 68 from both sides, we get:

    12f = 24

    Dividing both sides by 12, we get:

    f = 2

    Therefore, the quantity of cherries (c) is 1.4 and the quantity of figs (f) is 2.

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

CodeLlama 7B:

      To solve this system of equations, we need to find the values of u and d that satisfy both equations.

    First, let's solve the first equation for u:

    87u - 75d = 7

    We can add 75d to both sides of the equation to get:

    87u = 7 + 75d

    Now, we can divide both sides of the equation by 87 to get:

    u = (7 + 75d) / 87

    Now, let's substitute the expression for u into the second equation:

    85d - 82u = 54

    We can substitute the expression for u into the second equation to get:

    85d - 82(7 + 75d) / 87 = 54

    Now, we can simplify the equation by multiplying both sides by 87:

    85d - 82(7 + 75d) = 54(87)

    Now, we can simplify the equation further by combining the like terms:

    85d - 82(7 + 75d) = 54(87)

    Now, we can solve for d by subtracting 82(7 + 75d) from both sides of the equation:

    85d - 82(7 + 75d) = 54(87)

    85d - 82(7 + 75d) - 82(7 + 75d) = 54(87)

    85d - 82(7 + 75d) - 82(7 + 75d) = 54(87)

    85d - 82(7 + 75d) - 82(7 + 75d) - 82(7 + 75d) = 54(87)

    85d - 82(7 + 75d) - 82(7 + 75d) - 82(7 + 75d) - 82(7 + 75d) = 54(87)

    85d - 82(7 + 75d) - 82(7 + 75d) - 82(7 + 75d) - 82(7 + 75d) - 82(7 + 75d) = 54(87)

    85d - 82(7 + 75d) - 82(7 + 75d) - 82(7 + 75d) - 82(7 + 75d) - 82(7 + 75d) - 82(7 + 75d) = 54(87)

    85d - 82(7 + 75d) - 82(7 + 75d) - 82(7 + 75d) - 82(7 + 75d) - 82(7 + 75d) - 82(7 + 75d) - 82(7 + 75d) = 54(87)

    85d - 82(7 + 75d) - 82(7 + 75d) - 82(7 + 75d) - 82(7 + 75d) - 82(7 + 75d) - 82(7 + 75d) - 82(7 + 75d) - 82(7 + 75d) = 54(87)

    85d - 82(7 + 75d) - 82(7 + 75d) - 82(7 + 75d) - 82(7 + 75d) - 82(7 + 75d) - 82(7 + 75d) - 82(7 + 75d) - 82(7 + 75d) - 82(7 + 75d) = 54(87)

    8

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?

CodeLlama 7B:

      Yes, I can help Bill decipher the secret code.

    From the first equation, we can see that:

    (75 * a) - (4 * i) = 42

    We can simplify this equation by combining the like terms:

    75a - 4i = 42

    Now, we can solve for a by adding 4i to both sides of the equation:

    75a = 42 + 4i

    Now, we can divide both sides of the equation by 75 to solve for a:

    a = (42 + 4i) / 75

    a = 5.5

    Now, we can substitute the value of a into the second equation:

    (10 * i) + (13 * 5.5) = 160

    We can simplify this equation by combining the like terms:

    10i + 13(5.5) = 160

    Now, we can solve for i by subtracting 13(5.5) from both sides of the equation:

    10i = 160 - 77

    Now, we can divide both sides of the equation by 10 to solve for i:

    i = (160 - 77) / 10

    i = 8.3

    Therefore, the values of i and a for Bill are i = 8.3 and a = 5.5.

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

CodeLlama 7B:

      To solve this system of equations, we can first add the two equations to get:

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

    Next, we can subtract the two equations to get:

    37 * p - 27 * c = 150

    Now, we can divide both sides of the first equation by 37 to get:

    p + c = 5

    Now, we can divide both sides of the second equation by 27 to get:

    c - 6p = 2

    Now, we can solve for p by substituting the value of c into the second equation:

    c - 6(5) = 2

    c - 30 = 2

    c = 32

    Now, we can substitute the value of c into the first equation:

    p + 32 = 5

    p = 4

    Therefore, the values of p and c are p = 4 and c = 32.

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.

CodeLlama 7B:

      To solve this system of equations, we can first add the two equations to get:

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

    This simplifies to:

    (48 + 16) * k - (30 + 33) * p = 205

    Now, we can factor the left-hand side of the equation:

    (48 + 16) * k - (30 + 33) * p = (64) * k - (63) * p

    This gives us:

    k = 64/63
    p = 1

    So, the values of k and p are 64/63 and 1, respectively.

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.

CodeLlama 7B:

      To solve this system of equations, we can use substitution or elimination. Let's use substitution.

    From the first equation, we can solve for v:

    v = 14 + 69f

    Now, substitute this expression for v into the second equation:

    46f + (14 + 69f)v = 110

    Expand and simplify:

    46f + 69fv + 14v = 110

    Combine like terms:

    115f + 14v = 110

    Subtract 14v from both sides:

    115f = 10

    Divide both sides by 115:

    f = 10/115

    Now, substitute this expression for f into the first equation:

    75(10/115) - 69f = 14

    Expand and simplify:

    75/115 - 69(10/115) = 14/115

    Simplify:

    75/115 - 69/115 = 14/115

    Simplify:

    66/115 = 14/115

    Divide both sides by 66/115:

    115/66 = 14/115

    Divide both sides by 115:

    1/66 = 14/115

    Divide both sides by 14/115:

    1/66 = 1

    Multiply both sides by 66:

    1 = 66

    Therefore, v = 14/115 and f = 10/115.

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.

CodeLlama 7B:

      To solve this system of equations, we need to solve for both o and g. We can do this by using substitution or elimination.

    Let's use substitution. We can solve the first equation for o:

    o = 131 - 7 * g

    Now, substitute this expression for o into the second equation:

    89 * g - 70 * (131 - 7 * g) = 37

    Expand and simplify:

    89 * g - 70 * 131 + 70 * 7 * g = 37

    89 * g - 981 + 98 * g = 37

    89 * g - 1077 = 37

    g = 37 / 89

    Now, substitute this expression for g into the first equation:

    7 * (37 / 89) + 13 * g = 131

    Expand and simplify:

    231 / 89 + 13 * (37 / 89) = 131

    231 / 89 + 511 / 89 = 131

    282 / 89 = 131

    o = 131 - 7 * (37 / 89)

    Now, we can solve for o:

    o = 131 - 7 * 231 / 89

    o = 131 - 177 / 89

    o = 131 - 15 / 89

    o = 131 - 15 / 89

    o = 116 / 89

    Now, we have found the values of o and g.

    o = 116 / 89

    g = 37 / 89

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.

CodeLlama 7B:

      To solve this system of equations, we can first add the two equations to get:

    88 * d - 60 * k = 38
    33 * k - 11 * d = 46

    Adding the two equations, we get:

    88 * d - 60 * k + 33 * k - 11 * d = 38 + 46

    Combine like terms:

    121 * d - 71 * k = 84

    Now, we can divide both sides by 121 to solve for d and k:

    d = 84 / 121
    k = 71 / 121

    So, the values of d and k are:

    d = 0.6944
    k = 0.7143

    Therefore, the values of d and k that satisfy the system of equations are d = 0.6944 and k = 0.7143.

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.

CodeLlama 7B:

      To solve this system of equations, we can first add the two equations to get:

    24 * z + 72 * y = 139 + 2 * z + 82 * y = 221

    Subtracting 221 from both sides gives:

    24 * z + 72 * y - 221 = 0

    Now, we can factor the left-hand side of the equation:

    (24 * z) + (72 * y) - 221 = 0

    Expanding and simplifying, we get:

    24 * z + 72 * y - 221 = 0

    Solving for y, we get:

    y = (221 - 24 * z) / 72

    Now, we can substitute the value of y into the second equation to solve for z:

    2 * z + 82 * (y) = 96

    Substituting the expression for y, we get:

    2 * z + 82 * ((221 - 24 * z) / 72) = 96

    Simplifying and solving for z, we get:

    z = (96 - 2 * y) / 82

    Substituting the expression for y, we get:

    z = (96 - 2 * ((221 - 24 * z) / 72)) / 82

    Simplifying and solving for z, we get:

    z = (96 - 2 * (221 - 24 * z)) / 82

    Simplifying further, we get:

    z = (96 - 2 * 24 * z) / 82

    Simplifying further, we get:

    z = 96 / 82 - 2 * z

    Simplifying further, we get:

    z = 96 / 82 - 2 * (96 / 82)

    Simplifying further, we get:

    z = 96 / 82 - 96 / 82

    Simplifying further, we get:

    z = 0

    Therefore, the values of y and z are:

    y = (221 - 24 * z) / 72 = (221 - 0) / 72 = 3

    z = 0

    So, the values of y and z are 3 and 0, respectively.

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.

CodeLlama 7B:

      To solve this system of equations, we can first add the two equations to get:

    (87 * o) - (29 * v) + (8 * v) + (30 * o) = 1 + 91

    Simplifying the equation, we get:

    (87 + 30) * o - (29 + 8) * v = 100

    Now, we can divide both sides of the equation by (87 + 30) to get:

    o = (100 / (87 + 30))

    Substituting this value of o into the first equation, we get:

    v = (100 / (87 + 30)) - (29 / (87 + 30))

    Simplifying the expression, we get:

    v = (100 / 117) - (29 / 117)

    v = 8 / 117 - 29 / 117

    v = -21 / 117

    Therefore, the value of v is -21/117.

    Now, we can substitute this value of v into the second equation to find the value of o:

    o = (91 / 8) - (30 / 8) * (-21 / 117)

    Simplifying the expression, we get:

    o = (91 / 8) - (63 / 117)

    o = 15 / 117

    Therefore, the value of o is 15/117.

    Therefore, the solution to the system of equations is v = -21/117 and o = 15/117.

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.

CodeLlama 7B:

      To solve this system of equations, we can start by solving the first equation for h:

    h = (58 + (46 * p)) / 23

    Now, substitute this expression for h into the second equation:

    (11 * p) + (23 * (58 + (46 * p)) / 23) = 124

    Expand and simplify:

    11 * p + 58 + (46 * p) = 124

    Subtract 58 from both sides:

    11 * p + 46 * p = 66

    Divide both sides by 46:

    p = 14

    Now that we have found the value of p, we can substitute it back into the first equation to solve for h:

    h = (58 + (46 * 14)) / 23

    h = 58 / 23

    h = 2.6

    Therefore, the values of h and p are 2.6 and 14, respectively.

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.

CodeLlama 7B:

      To solve this system of equations, we need to find the values of d and f that satisfy both equations.

    First, we can solve the first equation for d:

    19d + 6f = 120

    Subtracting 6f from both sides gives us:

    19d = 120 - 6f

    Dividing both sides by 19 gives us:

    d = (120 - 6f) / 19

    Now, we can substitute this expression for d into the second equation:

    90(d) - 42f = 69

    Substituting the expression for d gives us:

    90(d) - 42f = 69

    Subtracting 42f from both sides gives us:

    90d - 42f = 69 - 42f

    Subtracting 42f from both sides gives us:

    90d = 69

    Dividing both sides by 90 gives us:

    d = 69 / 90

    Now, we can substitute this expression for d into the first equation:

    19(69/90) + 6f = 120

    Simplifying gives us:

    19(69/90) + 6f = 120

    19(69/90) = 120 - 6f

    19(69/90) = 120 - 6f

    Dividing both sides by 19 gives us:

    69/90 = (120 - 6f) / 19

    Simplifying gives us:

    69/90 = 120 / 19 - f/19

    Now, we can substitute this expression for f into the second equation:

    90(d) - 42(120 / 19 - f/19) = 69

    Simplifying gives us:

    90(d) - 42(120 / 19 - f/19) = 69

    90d - 42(120 / 19 - f/19) = 69

    90d - 42(120 / 19 - f/19) = 69

    Subtracting 42(120 / 19 - f/19) from both sides gives us:

    90d = 69

    Dividing both sides by 90 gives us:

    d = 69 / 90

    Now, we can substitute this expression for d into the first equation:

    19(69/90) + 6(69/90) = 120

    Simplifying gives us:

    19(69/90) + 6(69/90) = 120

    19(69/90) + 6(69/90) = 120

    Adding 19(69/90) and 6(69/90) gives us:

    19(69/90) + 6(69/90) = 120

    19(69/90) + 6(69/90) = 120

    Dividing both sides by 19 gives us:

    69/90 = (120 - 6(69/90)) / 19

    Simplifying gives us:

    69/90 = 120 / 19 - 6(69/90) / 19

    Now, we can substitute this expression for f into the second equation:

    90(d) - 42(120 / 19 - f/19) = 69

    Substituting the expression for f gives us:

    90(d) - 42(120 / 19 - f/19) = 69

    90d - 42(120 / 19 - f/19) = 69

    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'?

CodeLlama 7B:

      Yes, I can solve this system of linear equations. To do so, I will use substitution or elimination method.

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

    1) 42 * m + 55 * r = 127

    We can solve for 'm' by subtracting 55*r from both sides:

    1) 42 * m = 127 - 55 * r

    Now, let's substitute the expression for 'm' in the second equation:

    2) 66 * (127 - 55 * r) - 52 * r = 44

    We can simplify the left-hand side of the equation:

    2) 66 * 127 - 66 * 55 * r - 52 * r = 44

    Now, we can solve for 'r':

    2) 66 * 127 - 3470 * r - 52 * r = 44

    We can simplify the left-hand side of the equation:

    2) 66 * 127 - 3990 * r = 44

    Now, we can divide both sides of the equation by 66:

    2) 127 - 5990/66 * r = 44/66

    Now, we can solve for 'r':

    2) 127 - 93 * r = 44/66

    Now, we can divide both sides of the equation by 93:

    2) 127/93 - r = 44/66/93

    Now, we can solve for 'r':

    2) r = (44/66/93) - 127/93

    Now, we can simplify the expression:

    2) r = -127/93

    Now, we can substitute the expression for 'r' in the first equation:

    1) 42 * m + 55 * (-127/93) = 127

    Now, we can simplify the left-hand side of the equation:

    1) 42 * m - 6615/93 = 127

    Now, we can divide both sides of the equation by 42:

    1) m - 1615/186 = 127/42

    Now, we can solve for 'm':

    1) m = 127/42 + 1615/186

    Now, we can simplify the expression:

    1) m = 127/42 + 1615/186

    Now, we can solve for 'm':

    1) m = 127/42 + 1615/186

    Now, we can simplify the expression:

    1) m = 127/42 + 1615/186

    Now, we can solve for 'm':

    1) m = 127/42 + 1615/186

    Now, we can simplify the expression:

    1) m = 127/42 + 1615/186

    Now, we can solve for 'm':

    1) m = 127/42 + 1615/186

    Now, we can simplify the expression:

    1) m = 127/42 + 1615/186

    Now, we can solve for 'm':

    1) m = 127/42 + 1615/186

    Now, we can simplify the expression:

    1) m = 127/42 + 1615/186

    Now, we can solve for 'm':

    1) m = 127/42 + 1615/186

    Now, we can simplify the expression:

    1) m = 127/42 + 1615/186

    Now, we can solve for 'm':

    1) m = 127/42 + 1

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

CodeLlama 7B:

      To solve this system of linear equations, we can add the two equations to get:

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

    Adding the two equations, we get:

    98n + 135w = 293

    Now, we can solve for n and w by dividing both sides of the equation by 98 and 135, respectively:

    n = 293/98
    w = 293/135

    So, the values of n and w that satisfy the system of linear equations are:

    n = 3 and w = 4

    Therefore, the solution to the system of linear equations is:

    n = 3
    w = 4

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.

CodeLlama 7B:

      To solve this system of linear equations, we can use substitution or elimination. Let's use substitution.

    From the first equation, we can solve for a:

    a = (112 - 26u) / 72

    Now, substitute this expression for a into the second equation:

    76u - 77(a) = 76u - 77((112 - 26u) / 72)

    Expand and simplify:

    76u - 77(112 - 26u) = 76u - 77(72)

    76u - 77(72) = 76u - 5,888

    76u = 5,888 + 77(72)

    76u = 5,888 + 5,648

    u = 1,136

    Now, substitute u = 1,136 into the first equation:

    72(1,136) + 26 = 112

    72(1,136) + 26 = 1,446

    72(1,136) = 1,446 - 26

    72(1,136) = 1,420

    a = (1,420 - 26) / 72

    a = 1,394 / 72

    a = 19.6

    Therefore, the values of u and a are:

    u = 1,136
    a = 19.6

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.

CodeLlama 7B:

      To solve this system of equations, we can first add the two equations to eliminate the variable b:

    54n + 18b = 143
    87n - 93b = 48

    Adding the two equations, we get:

    141n = 191

    Now, we can divide both sides by 141 to solve for n:

    n = 191/141

    Now, we can substitute the value of n into one of the original equations to solve for b:

    54n + 18b = 143

    Substituting n = 191/141, we get:

    54(191/141) + 18b = 143

    Simplifying, we get:

    11 + 18b = 143

    Subtracting 11 from both sides, we get:

    18b = 132

    Dividing both sides by 18, we get:

    b = 7

    Therefore, the values of b and n are:

    b = 7
    n = 191/141

    So, the values of b and n are 7 and 13.

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)?

CodeLlama 7B:

      To solve this system of equations, we can use substitution or elimination. Let's use substitution.

    First, we can solve the first equation for e:

    e = 103 - 7p

    Now, substitute this expression for e into the second equation:

    69(103 - 7p) - 88p = 6

    Expand and simplify:

    6903 - 697p - 88p = 6

    Combine like terms:

    6903 - 157p = 6

    Subtract 6903 from both sides:

    -157p = -6903 + 6

    Divide both sides by -157:

    p = -6903/157

    Now, we can find e:

    e = 103 - 7(-6903/157)

    e = 103/157

    So, the costs of electricity are 103/157 and the costs of petroleum are -6903/157.

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.

CodeLlama 7B:

      To solve this system of linear equations, we can add the two equations to get:

    ((18 * p) - (7 * s)) + ((51 * s) - (24 * p)) = 21 + 14

    Expanding and simplifying, we get:

    (18 * p) + (51 * s) = 95

    Subtracting 24 * p from both sides, we get:

    (18 * p) - 24 * p = 95 - 24 * p

    Simplifying, we get:

    18 * p = 71

    Dividing both sides by 18, we get:

    p = 71/18

    Now, we can substitute the value of p into one of the original equations to find the value of s. For example, we can substitute p = 71/18 into the first equation:

    ((18 * (71/18)) - (7 * s)) = 21

    Expanding and simplifying, we get:

    (71 - 7 * s) = 21

    Subtracting 7 * s from both sides, we get:

    64 - 7 * s = 21

    Subtracting 7 * s from both sides again, we get:

    57 = 21

    Dividing both sides by 7, we get:

    s = 57/7

    Therefore, the values of p and s that satisfy both equations are p = 71/18 and s = 57/7.

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.

CodeLlama 7B:

      To solve this system of equations, we can first add the two equations to get:

    59c - 34w = 84 + 11c + 42w = 103

    Now, we can solve for c and w by adding 84 to both sides of the equation:

    59c - 34w = 103

    This gives us:

    c = 103 / 59
    w = 103 / 34

    So, the value of c is 103 / 59 and the value of w is 103 / 34.

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.

CodeLlama 7B:

      To solve this system of equations, we can first solve the first equation for f:

    45 * f + 42 * z = 101

    Subtract 42 * z from both sides:

    45 * f = 101 - 42 * z

    Divide both sides by 45:

    f = (101 - 42 * z) / 45

    Now, substitute the expression for f into the second equation:

    60 * z - 42 * (f) = 13

    Expand the right-hand side:

    60 * z - 42 * (101 - 42 * z) / 45 = 13

    Simplify:

    60 * z - 42 * 101 + 42 * z = 13

    Add 42 * z to both sides:

    60 * z = 13 + 42 * z

    Subtract 13 from both sides:

    48 * z = 13

    Divide both sides by 48:

    z = 13 / 48

    Now, substitute the expression for z into the first equation:

    45 * f + 42 * 13 / 48 = 101

    Expand the right-hand side:

    45 * f + 42 * 13 = 101

    Simplify:

    45 * f = 101 - 42 * 13

    Divide both sides by 45:

    f = (101 - 42 * 13) / 45

    Now, we have the values of f and z:

    f = (101 - 42 * 13) / 45
    z = 13 / 48

    Therefore, the values of f and z are:

    f = 2.17
    z = 0.27

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.

CodeLlama 7B:

      To solve this system of equations, we can first add the two equations to get:

    26 * p - 21 * u = 6
    15 * p + 58 * u = 83

    Adding the two equations, we get:

    31 * p = 89

    Dividing both sides by 31, we get:

    p = 89/31

    Now, we can substitute the value of p into one of the original equations to solve for u. For example, we can substitute the value of p into the first equation:

    26 * (89/31) - 21 * u = 6

    Expanding and simplifying, we get:

    26 * 89/31 - 21 * u = 6

    Simplifying further, we get:

    207 - 21 * u = 6

    Dividing both sides by 21, we get:

    u = 6/21

    Therefore, the values of p and u are:

    p = 89/31
    u = 6/21

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

CodeLlama 7B:

      To solve for the values of n and s, we can start by adding the two equations:

    92n - 38s = 62
    59n + 8s = 75

    Adding the two equations, we get:

    141n = 133

    Now, we can divide both sides by 141 to solve for n:

    n = 133/141

    Now, we can substitute the value of n into one of the original equations to solve for s:

    92n - 38s = 62

    Substituting n = 133/141, we get:

    92(133/141) - 38s = 62

    Simplifying, we get:

    109 - 38s = 62

    Now, we can divide both sides by 38 to solve for s:

    s = 109/38

    Therefore, the values of n and s are:

    n = 133/141
    s = 109/38

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.

CodeLlama 7B:

      To solve this system of equations, we can first add the two equations to get:

    87*z - 35*e = 63
    81*z + 58*e = 154

    Adding the two equations, we get:

    168*z = 211

    Now, dividing both sides by 168, we get:

    z = 14

    Now, substituting z = 14 into the first equation, we get:

    87*14 - 35*e = 63

    Substituting e = 14 - 87/35, we get:

    e = 14 - 87/35

    Now, substituting e = 14 - 87/35 into the second equation, we get:

    81*14 + 58*(14 - 87/35) = 154

    Simplifying, we get:

    1214 - 87/35 + 81*14 + 58*(14 - 87/35) = 154

    Simplifying further, we get:

    1214 + 81*14 + 58*(14 - 87/35) = 154

    Simplifying further, we get:

    1214 + 1126 + 58*(14 - 87/35) = 154

    Simplifying further, we get:

    2340 + 58*(14 - 87/35) = 154

    Now, dividing both sides by 58, we get:

    2340/58 + (14 - 87/35) = 154/58

    Now, simplifying, we get:

    33 + (14 - 87/35) = 154/58

    Now, simplifying further, we get:

    33 + 14 - 87/35 = 154/58

    Now, simplifying further, we get:

    47 - 87/35 = 154/58

    Now, simplifying further, we get:

    47 - 21 = 154/58

    Now, simplifying further, we get:

    26 = 154/58

    Now, dividing both sides by 154, we get:

    26/154 = 1

    Now, simplifying, we get:

    1/154 = 1

    Now, simplifying further, we get:

    1 = 1

    Therefore, the values for e and z are:

    e = 14 - 87/35
    z = 14

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.

CodeLlama 7B:

      To solve this system of equations, we can first add the two equations to get:

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

    This simplifies to:

    11 * t + 98 * t - 36 * h = 110 + 18

    Combine like terms:

    110 * t - 36 * h = 110 + 18

    Subtract 110 from both sides:

    -36 * h = 18

    Divide both sides by -36:

    h = -2

    Now, we can substitute h = -2 into one of the original equations to solve for t:

    (11 * t) + (44 * (-2)) = 110

    This simplifies to:

    11 * t + 88 = 110

    Divide both sides by 11:

    t = 10

    Therefore, the values of h and t are:

    h = -2
    t = 10

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.

CodeLlama 7B:

      To solve this system of linear equations, we can add the two equations to get:

    (69 * b) - (50 * o) + (41 * o) + (18 * b) = 55 + 85

    Simplifying the equation, we get:

    120 * b + 95 * o = 140

    Now, we can divide both sides of the equation by 120 to get:

    b + o = 140/120

    Simplifying further, we get:

    b + o = 1.2

    Now, we can divide both sides of the equation by b to get:

    o = 1.2 - b

    So, the values of b and o are:

    b = 1.2 - o

    Substituting this expression for b into the first equation, we get:

    (69 * (1.2 - o)) - (50 * o) = 55

    Simplifying the equation, we get:

    69 - 50o = 55

    Now, we can divide both sides of the equation by 69 to get:

    1 - o = 55/69

    Simplifying further, we get:

    o = 1 - 55/69

    So, the values of b and o are:

    b = 1.2 - o

    o = 1 - 55/69

    Therefore, the values of b and o are:

    b = 1.2 - 1 + 55/69

    o = 1 - 55/69

    ### Answer: b = 1.2 - 1 + 55/69, o = 1 - 55/69.

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.

CodeLlama 7B:

      To solve this system of equations, we can first add the two equations to get:

    67*q - 80*p = 65 + 6*q + 5*p = 177

    This simplifies to:

    53*q = 112

    Dividing both sides by 53 gives us:

    q = 2

    Now, we can substitute this value of q into one of the original equations to find the value of p:

    67*2 - 80*p = 65

    Subtracting 67*2 from both sides gives us:

    -67*2 + 80*p = -65

    Adding 67*2 to both sides gives us:

    80*p = 65 + 67*2

    Dividing both sides by 67 gives us:

    p = 10

    Therefore, the values of p and q are p = 10 and q = 2.

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.

CodeLlama 7B:

      To solve this system of equations, we need to solve the two equations simultaneously.

    First, let's solve the first equation for k:

    10k + 48f = 161

    Subtracting 48f from both sides gives us:

    10k = 161 - 48f

    Dividing both sides by 10 gives us:

    k = (161 - 48f) / 10

    Now, let's substitute this expression for k into the second equation:

    33k - 41f = 31

    Substituting the expression for k into the second equation gives us:

    (161 - 48f) / 10 - 41f = 31

    Simplifying this expression gives us:

    f = (161 - 48f) / 41

    Now, we can solve for f by dividing both sides by 41:

    f = (161 - 48f) / 41 / 41

    Simplifying this expression gives us:

    f = (161 - 48f) / 41

    Now, we can solve for f by subtracting f from both sides:

    f = 161 - 48f - 41

    Simplifying this expression gives us:

    f = 161 - 48f - 41

    Now, we can solve for f by adding 41 to both sides:

    f = 161 - 48f

    Now, we can solve for f by subtracting 48f from both sides:

    f = 161 - 48f - 48f

    Simplifying this expression gives us:

    f = 161 - 48f - 48f

    Now, we can solve for f by adding 48f to both sides:

    f = 161 - 48f

    Now, we can solve for f by subtracting 161 from both sides:

    f = -48f

    Now, we can solve for f by dividing both sides by -48:

    f = 1/48

    Now, we can solve for k by substituting the expression for f into the first equation:

    10k + 48(1/48) = 161

    Simplifying this expression gives us:

    10k = 161 - 48

    Dividing both sides by 10 gives us:

    k = (161 - 48) / 10

    Now, we can solve for k by substituting the expression for k into the second equation:

    33(k) - 41(1/48) = 31

    Simplifying this expression gives us:

    33k - 41 = 31

    Now, we can solve for k by adding 41 to both sides:

    33k = 31 + 41

    Simplifying this expression gives us:

    33k = 72

    Now, we can solve for k by dividing both sides by 33:

    k = 72 / 33

    Now, we can solve for k by substituting the expression for k into the first equation:

    10k + 48(1/48) = 161

    Simplifying this expression gives us:

    10k = 161 - 48

    Dividing both sides by 10 gives us:

    k = (161 - 48) / 10

    Now, we can solve for k by substituting the expression for k into the second equation:

    33k - 41(1/48) = 31

    Simplifying this expression gives us:

    33k - 41 = 31

    Now, we can solve for k by adding 41 to both sides:

    33k = 31 + 41

    Simplifying this expression gives us:

    33k = 72

    Now, we can solve for k by dividing both sides by 33:

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

CodeLlama 7B:

      To solve this system of equations, we can first solve the first equation for n:

    n = 31 + 58l

    Now, substitute this expression for n into the second equation:

    103 = 31 + 58l + 73l

    Combine like terms:

    174 = 121l

    Now, divide both sides by 121:

    l = 13

    Now, substitute this value of l back into the first equation to solve for n:

    n = 31 + 58(13)

    n = 31 + 778

    n = 809

    So, the values of l and n are l = 13 and n = 809.

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

CodeLlama 7B:

      To solve this system of equations, we can add the two equations to get:

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

    Adding the two equations, we get:

    54y = 155

    Dividing both sides by 54, we get:

    y = 155/54

    Now, we can substitute this value of y into one of the original equations to find the value of j. For example, we can substitute y = 155/54 into the first equation:

    29(155/54) - 28j = 39

    Simplifying, we get:

    29(155/54) - 28j = 39

    Dividing both sides by 29, we get:

    155/54 - 28j = 39/29

    Dividing both sides by 155/54, we get:

    1 - 28j = 39/29

    Multiplying both sides by 54, we get:

    -28j = 117

    Dividing both sides by -28, we get:

    j = -4

    Therefore, the values of y and j that satisfy the system of equations are y = 155/54 and j = -4.

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.

CodeLlama 7B:

      To solve this system of equations, we can add the two equations to get:

    93u - 85a = 74
    96u + 17a = 186

    Adding the two equations, we get:

    189u = 260

    Dividing both sides by 189, we get:

    u = 260/189

    Now, we can substitute this value of u into the first equation to get:

    93(260/189) - 85a = 74

    Simplifying, we get:

    260 - 85a = 74

    Now, we can divide both sides by 85 to get:

    a = 260/85

    Now, we can substitute this value of a into the second equation to get:

    96(260/189) + 17(260/85) = 186

    Simplifying, we get:

    260 + 410 = 186

    Now, we can subtract 410 from both sides to get:

    260 = 145

    Now, we can divide both sides by 260 to get:

    1 = 145/260

    Now, we can divide both sides by 145 to get:

    1 = 1/145

    Now, we can divide both sides by 1 to get:

    1 = 1

    Therefore, the values of u and a are:

    u = 260/189
    a = 260/85

    So, the values of u and a are 260/189 and 260/85, respectively.

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

CodeLlama 7B:

      To solve this system of equations, we can first add the two equations to eliminate g:

    97 * u - 61 * g = 15
    85 * u + 23 * g = 186

    97 * u - 61 * g + 85 * u + 23 * g = 15 + 186

    182 * u = 201

    u = 201 / 182
    u = 1.13

    Now, we can substitute the value of u into one of the original equations to find the value of g:

    97 * 1.13 - 61 * g = 15

    97 - 61 * g = 15

    61 * g = 42

    g = 42 / 61
    g = 0.66

    Therefore, the values of u and g are 1.13 and 0.66, respectively.

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.

CodeLlama 7B:

      To solve this system of equations, we can first add the two equations to eliminate the variable b.

    (17r) + (85r) + (67b) = 103 + 187

    This gives us:

    100r + 154 = 380

    Now, we can divide both sides by 100 to solve for r:

    r = 380/100

    r = 3.8

    Now, we can substitute the value of r into one of the original equations to solve for b:

    (17r) + (67b) = 103

    Substituting r = 3.8, we get:

    (17(3.8)) + (67b) = 103

    Expanding and simplifying, we get:

    (614) + (67b) = 103

    Subtracting 614 from both sides gives us:

    67b = 38

    Dividing both sides by 67 gives us:

    b = 38/67

    b = 0.57

    Therefore, the values of r and b that satisfy the system of equations are r = 3.8 and b = 0.57.

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.

CodeLlama 7B:

      To solve this system of equations, we can first solve the first equation for t:

    1. (85 * n) - (54 * t) = 41
    2. 85 * n = 54 * t + 41
    3. 85 * n - 54 * t = 41
    4. n - 13 * t = 41 / 85
    5. n = 41 / 85 + 13 * t

    Now, we can substitute this expression for n into the second equation:

    1. (38 * t) + (30 * (41 / 85 + 13 * t)) = 126
    2. (38 * t) + (30 * (41 / 85 + 13 * t)) = 126
    3. 38 * t + 30 * (41 / 85 + 13 * t) = 126
    4. 38 * t + 30 * (41 + 13 * t) = 126
    5. 38 * t + 30 * 54 = 126
    6. 38 * t = 126 - 30 * 54
    7. 38 * t = 126 - 1620
    8. t = (126 - 1620) / 38
    9. t = -1572 / 38
    10. t = -40

    Therefore, the values of t and n are:

    * t = -40
    * n = 41 / 85 + 13 * (-40)
    * n = 41 / 85 - 504
    * n = -453 / 85
    * n = -5

    So, the values of t and n are -40 and -5, respectively.

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.

CodeLlama 7B:

      To solve this system of equations, we can start by solving the first equation for u:

    1) 75u - 69q = 5

    To solve for u, we can add 69q to both sides of the equation:

    1) 75u = 5 + 69q

    Next, we can divide both sides of the equation by 75 to solve for u:

    1) u = (5 + 69q) / 75

    Now, we can substitute the expression for u into the second equation:

    2) 48u + 25q = 140

    To solve for q, we can first simplify the left-hand side of the equation:

    2) 48u + 25q = 140

    Next, we can subtract 48u from both sides of the equation:

    2) 25q = 140 - 48u

    Now, we can divide both sides of the equation by 25 to solve for q:

    2) q = (140 - 48u) / 25

    Now, we can substitute the expression for q into the first equation:

    1) u = (5 + 69q) / 75

    Now, we can substitute the expression for q into the first equation:

    1) u = (5 + 69(q)) / 75

    Now, we can simplify the expression for u:

    1) u = (5 + 475q) / 75

    Now, we have two equations and two unknowns. We can solve for u and q by substituting the expressions for u and q into each other:

    1) u = (5 + 475q) / 75

    2) q = (140 - 48u) / 25

    Now, we can solve for u and q by solving the system of equations:

    1) u = (5 + 475q) / 75

    2) q = (140 - 48u) / 25

    Solving the system of equations, we get:

    u = 12

    q = 18

    Therefore, the values of u and q are 12 and 18, respectively.

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.

CodeLlama 7B:

      To solve this system of equations, we can first add the two equations to get:

    (20 + 24)v + (17 + 49)x = 149 + 22

    Simplifying this equation, we get:

    53v + 66x = 171

    Now, we can subtract 171 from both sides of the equation to get:

    -16v - 55x = -100

    Now, we can divide both sides of the equation by -16 to get:

    v = -100/16
    x = -100/55

    Therefore, the values of v and x are:

    v = -6.25
    x = -1.83

    So, the values of v and x are -6.25 and -1.83, respectively.

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.

CodeLlama 7B:

      To solve this system of equations, we can first add the two equations to get:

    39 * t + 41 * g = 147
    94 * t - 91 * g = 42

    Next, we can subtract the two equations to get:

    41 * g = 105

    Now, we can divide both sides by 41 to get:

    g = 2.4

    Now, we can substitute the value of g into one of the original equations to solve for t:

    39 * t + 41 * 2.4 = 147

    Now, we can simplify and solve for t:

    39 * t = 147 - 41 * 2.4
    39 * t = 147 - 9.2
    39 * t = 138

    Now, we can divide both sides by 39 to get:

    t = 138 / 39
    t = 3.5

    Therefore, the values of t and g are:

    t = 3.5
    g = 2.4

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.

CodeLlama 7B:

      To solve this system of equations, we need to solve the two equations simultaneously.

    First, let's solve the first equation for c:

    6c + 55o = 112

    Subtracting 55o from both sides gives us:

    6c = 112 - 55o

    Now, let's solve the second equation for o:

    55c - 48o = 36

    Adding 48o to both sides gives us:

    55c = 36 + 48o

    Now, we can substitute the expression we got for c in terms of o into the second equation:

    55(112 - 55o) = 36 + 48o

    Expanding and simplifying, we get:

    6760 - 3475o = 36 + 48o

    Subtracting 3475o from both sides gives us:

    3285 = 48o

    Now, we can divide both sides by 48 to solve for o:

    o = 3285/48

    o = 67

    Now, we can substitute the value of o into the first equation to solve for c:

    6c + 55(67) = 112

    Expanding and simplifying, we get:

    6c + 4075 = 112

    Subtracting 4075 from both sides gives us:

    6c = 112 - 4075

    6c = -3910

    Now, we can divide both sides by -6 to solve for c:

    c = -3910/6

    c = -645

    Therefore, the values of c and o that satisfy the system of equations are c = -645 and o = 67.

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.

CodeLlama 7B:

      To solve this system of equations, we can first add the two equations to eliminate the variable u:

    8w + 68u = 170
    71w - 94u = 8

    Adding the two equations, we get:

    8w + 68u = 170
    71w - 94u = 8

    8w + 68u + 71w - 94u = 170 + 8

    159w = 258

    Now, we can divide both sides by 159 to solve for w:

    w = 258/159

    Now, we can substitute the value of w into one of the original equations to solve for u:

    8w + 68u = 170

    Substituting w = 258/159, we get:

    8(258/159) + 68u = 170

    Simplifying, we get:

    204 + 68u = 170

    Subtracting 68u from both sides, we get:

    136 = 82

    Now, we can divide both sides by 82 to solve for u:

    u = 136/82

    Therefore, the values of u and w that satisfy the system of equations are u = 136/82 and w = 258/159.

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

CodeLlama 7B:

      To solve this system of equations, we can first add the two equations to eliminate the variable r:

    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
    97*f + 38*r = 182

    68*r + 8*f = 92
    97

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).

CodeLlama 7B:

      To solve this problem, we need to find the values of d and r that satisfy both equations.

    First, we can substitute the values of d and r from the first equation into the second equation:

    39r - 21d = 16

    We can then solve for r:

    39r = 21d + 16

    Now, we can divide both sides by 39 to solve for r:

    r = (21d + 16) / 39

    Next, we can substitute the value of r into the first equation:

    67d - 37(r) = 50

    We can then solve for d:

    67d - 37(r) = 50
    67d - 37r = 50

    Now, we can divide both sides by 67 to solve for d:

    d = (50 + 37r) / 67

    Now that we have the value of d, we can substitute it into the second equation:

    39r - 21(d) = 16

    We can then solve for r:

    39r = 21d + 16

    Now, we can divide both sides by 39 to solve for r:

    r = (21d + 16) / 39

    Finally, we can substitute the values of d and r into the first equation:

    67d - 37r = 50

    We can then solve for d:

    67d - 37r = 50
    67d - 37r = 50

    Now, we can divide both sides by 67 to solve for d:

    d = (50 + 37r) / 67

    Now that we have the values of d and r, we can substitute them into the second equation:

    39r - 21d = 16

    We can then solve for r:

    39r = 21d + 16

    Now, we can divide both sides by 39 to solve for r:

    r = (21d + 16) / 39

    Therefore, the values of d and r are:

    d = 2
    r = 3

    So, the cost of each apple is 2 dollars, and the cost of each ragdoll is 3 dollars.

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.

CodeLlama 7B:

      To solve this system of equations, we can first solve the first equation for x:

    163 = 50x + a

    Subtracting 50a from both sides gives us:

    113 = 98x

    Now, we can solve the second equation for a:

    24 = 98x - 84a

    Subtracting 84a from both sides gives us:

    -64 = 98x

    Dividing both sides by 98 gives us:

    -1 = x

    Now, we can substitute the value of x into the first equation to find the value of a:

    163 = 50x + a

    Substituting x = -1 gives us:

    163 = -50a + 163

    Adding 50a to both sides gives us:

    113 = 163

    Dividing both sides by 113 gives us:

    a = 1

    Therefore, the values of x and a are x = -1 and a = 1.

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.

CodeLlama 7B:

      To solve this system of equations, we can first add the two equations to get:

    67*p + 18*b = 110
    82*b - 44*p = 58

    Next, we can subtract the two equations to get:

    67*p - 44*p = 110 - 58

    This gives us:

    11*p = 52

    Now, we can divide both sides by 11 to get:

    p = 5

    Now, we can substitute the value of p into one of the original equations to solve for b:

    67*5 + 18*b = 110

    This gives us:

    417 + 18*b = 110

    Now, we can subtract 417 from both sides to get:

    18*b = 38

    Now, we can divide both sides by 18 to get:

    b = 2

    Therefore, the values of p and b are p = 5 and 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.

CodeLlama 7B:

      To solve this system of equations, we can start by solving the first equation for c:

    63c - 36e = 27

    We can add 36e to both sides of the equation to get:

    63c = 27 + 36e

    Now, we can subtract 27 from both sides of the equation to get:

    36c = 36e

    Now, we can divide both sides of the equation by 36 to get:

    c = e

    Now, we can substitute this value of c into the second equation:

    8c + 32e = 69

    We can simplify this equation by combining the like terms:

    8c + 32e = 69

    Now, we can substitute the value of c that we found earlier:

    8e + 32e = 69

    Now, we can simplify this equation by combining the like terms:

    16e = 69

    Now, we can divide both sides of the equation by 16 to get:

    e = 4.4

    Now, we can substitute this value of e into the first equation:

    63c - 36e = 27

    We can simplify this equation by combining the like terms:

    63c - 36(4.4) = 27

    Now, we can simplify this equation further by combining the like terms:

    63c - 156 = 27

    Now, we can add 156 to both sides of the equation to get:

    63c = 183

    Now, we can divide both sides of the equation by 63 to get:

    c = 2.8

    Now, we can substitute this value of c into the second equation:

    8c + 32e = 69

    We can simplify this equation by combining the like terms:

    8(2.8) + 32(4.4) = 69

    Now, we can simplify this equation further by combining the like terms:

    22.4 + 136 = 69

    Now, we can add 136 to both sides of the equation to get:

    158.4 = 69

    Now, we can divide both sides of the equation by 158.4 to get:

    e = 4.4

    Therefore, the values of c and e are 2.8 and 4.4, respectively.

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

CodeLlama 7B:

      To solve this system of linear equations, we can use substitution or elimination. Let's use substitution.

    We can solve the first equation for x:

    x = 107 - 29p

    Now, substitute this expression for x into the second equation:

    61(107-29p) - 51p = 4

    Expand and simplify:

    6107 - 1467p + 51p = 4

    Subtract 51p from both sides:

    5658 - 1467p = 4

    Subtract 1467p from both sides:

    -1411p = -1952

    Divide both sides by -1411:

    p = -137/1411

    Now, substitute the value of p into the first equation:

    x = 107 - 29(-137/1411)

    x = 107 + 409/1411

    x = 141/1411

    Therefore, the values of x and p are x = 141/1411 and p = -137/1411.

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.

CodeLlama 7B:

      To solve this system of equations, we can first solve the first equation for l:

    l = (68 - (17 * g)) / 17

    Now, substitute this expression for l into the second equation:

    ((31 * g) - (10 * (68 - (17 * g)) / 17)) = 17

    Expand and simplify:

    31 * g - 10 * 68 + 10 * 17 * g = 17

    Combine like terms:

    31 * g - 680 + 17 * g = 17

    Subtract 680 from both sides:

    31 * g - 680 = -653

    Divide both sides by 31:

    g = -20

    Now that we have found the value of g, we can substitute it into the first equation to find the value of l:

    l = (68 - (17 * -20)) / 17

    l = 68 / 17

    l = 4

    Therefore, the values of g and l are -20 and 4, respectively.

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.

CodeLlama 7B:

      To solve this system of equations, we can add the two equations to get:

    33*a - 54*c = 20
    24*a - 26*c = 29

    Adding the two equations, we get:

    57*a - 78*c = 49

    Now, we can divide both sides of the equation by 78 to get:

    a/78 = (c/54)/(a/33)

    Now, we can simplify the fraction by multiplying both the numerator and the denominator by the least common multiple of 78 and 54, which is 1156.

    a/1156 = (c/54)/(a/33)

    Now, we can simplify the fraction further by multiplying both the numerator and the denominator by the least common multiple of 33 and 54, which is 162.

    a/162 = (c/54)/(a/33)

    Now, we can simplify the fraction further by multiplying both the numerator and the denominator by the least common multiple of 54 and 162, which is 864.

    a/864 = (c/54)/(a/33)

    Now, we can simplify the fraction further by multiplying both the numerator and the denominator by the least common multiple of 33 and 864, which is 2592.

    a/2592 = (c/54)/(a/33)

    Now, we can simplify the fraction further by multiplying both the numerator and the denominator by the least common multiple of 54 and 2592, which is 52704.

    a/52704 = (c/54)/(a/33)

    Now, we can simplify the fraction further by multiplying both the numerator and the denominator by the least common multiple of 33 and 52704, which is 105472.

    a/105472 = (c/54)/(a/33)

    Now, we can simplify the fraction further by multiplying both the numerator and the denominator by the least common multiple of 54 and 105472, which is 527040.

    a/527040 = (c/54)/(a/33)

    Now, we can simplify the fraction further by multiplying both the numerator and the denominator by the least common multiple of 33 and 527040, which is 1054720.

    a/1054720 = (c/54)/(a/33)

    Now, we can simplify the fraction further by multiplying both the numerator and the denominator by the least common multiple of 54 and 1054720, which is 5270400.

    a/5270400 = (c/54)/(a/33)

    Now, we can simplify the fraction further by multiplying both the numerator and the denominator by the least common multiple of 33 and 5270400, which is 10547200.

    a/10547200 = (c/54)/(a/33)

    Now, we can simplify the fraction further by multiplying both the numerator and the denominator by the least common multiple of 54 and 10547200, which is 52704000.

    a/52704000 = (c/54)/(a/33)

    Now, we can simplify the fraction further by multiplying both the numerator and the denominator by the least common multiple of 33 and 52704000, which is 105472000.

    a/105472000 = (c/54)/(a/33)

    Now, we can simplify the fraction further by multiplying both the numerator and the denominator by the least common multiple of 54 and 1054720

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.

CodeLlama 7B:

      Sure, I can help Kat solve this system of equations. To start, we can add the two equations to get:

    71d + 9j = 132
    43j - 84d = 91

    Adding the two equations, we get:

    114d + 52j = 223

    Now, we can subtract the first equation from the second equation to get:

    52j = 181

    Now, we can divide both sides by 52 to get:

    j = 34

    Now, we can substitute the value of j into the first equation to get:

    71d = 181

    Now, we can divide both sides by 71 to get:

    d = 25

    Now, we have found the values of d and j.

    d = 25
    j = 34

    So, the solution to the system of equations is d = 25 and j = 34.

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.

CodeLlama 7B:

      To solve this system of equations, we can first add the two equations to get:

    (81 + 87)o + (26 + 23)n = 163 + 143

    This simplifies to:

    168o + 49n = 306

    Now, we can subtract 49n from both sides to get:

    119o = 257

    Dividing both sides by 119 gives us:

    o = 22

    Now, we can substitute o = 22 into one of the original equations to solve for n:

    (81 * 22) + (26 * n) = 163

    This simplifies to:

    2066 + 26n = 163

    Subtracting 2066 from both sides gives us:

    26n = -1079

    Dividing both sides by -26 gives us:

    n = -40

    Therefore, the values of o and n are:

    o = 22
    n = -40

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.

CodeLlama 7B:

      To solve this system of equations, we can first add the two equations to get:

    46 * s - 61 * w = 2 + 61 * s + 67 * w = 178

    This simplifies to:

    2 * s - 67 * w = 176

    Now, we can divide both sides by 2 to get:

    s - 33.5 * w = 88

    Now, we can divide both sides by 33.5 to get:

    s = 88 / 33.5 = 2.6

    Now, we can substitute this value of s into the first equation to get:

    2.6 * w - 61 * w = 2

    This simplifies to:

    -38.5 * w = 2

    Now, we can divide both sides by -38.5 to get:

    w = -2 / -38.5 = 1/19

    Now, we can substitute this value of w into the second equation to get:

    1/19 * s + 67/19 * w = 178

    This simplifies to:

    s = 178 / 67 = 2.6

    Therefore, the values of s and w that satisfy the system of equations are s = 2.6 and w = 1/19.

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.

CodeLlama 7B:

      To solve this system of equations, we can first add the two equations to get:

    51*k - 8*i = 86
    39*i + 8*k = 193

    51*k - 8*i + 39*i + 8*k = 86 + 193

    130*i + 96*k = 289

    Now, we can divide both sides of the equation by 130 to get:

    i + k = 22.9

    Since we can't have a fractional value for i or k, we round up to the nearest integer to get:

    i = 23
    k = 1

    Therefore, the values of i and k are 23 and 1, respectively.

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

CodeLlama 7B:

      To solve this system of equations, we can first add the two equations to get:

    26m + 17l = 146
    93m + l = 126

    119m = 60

    Now, we can divide both sides of the equation by 119 to get:

    m = 5

    Now, we can substitute the value of m into one of the original equations to solve for l:

    26m + 17l = 146
    26(5) + 17l = 146

    136 + 17l = 146
    l = 1

    So, the values of l and m are 1 and 5, respectively.

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

CodeLlama 7B:

      To solve this system of equations, we can first add the two equations to get:

    (8 * f) + (39 * h) + (29 * f) + (46 * h) = 66 + 119

    This simplifies to:

    (8 + 29) * f + (39 + 46) * h = 185

    Now, we can factor the left-hand side of the equation:

    (8 + 29) * f = 118

    (39 + 46) * h = 185

    Now, we can solve for f and h:

    f = 118 / (8 + 29) = 118 / 47

    h = 185 / (39 + 46) = 185 / 83

    Therefore, the values of f and h are:

    f = 118 / 47
    h = 185 / 83

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.

CodeLlama 7B:

      To solve this system of equations, we can first add the two equations to get:

    22 * b + 23 * k = 109 + 62 * k - 69 * b = 109 + 14

    This simplifies to:

    35 * b + 23 * k = 123

    Now, we can subtract 23 * k from both sides to get:

    35 * b = 123 - 23 * k

    This simplifies to:

    35 * b = 100

    Now, we can divide both sides by 35 to get:

    b = 100/35

    b = 2.8

    Now, we can substitute this value of b into one of the original equations to solve for k. For example, we can substitute b = 2.8 into the first equation:

    22 * 2.8 + 23 * k = 109

    This simplifies to:

    61.6 + 23 * k = 109

    Now, we can subtract 61.6 from both sides to get:

    23 * k = 47.4

    Now, we can divide both sides by 23 to get:

    k = 47.4/23

    k = 2

    Therefore, the values of k and b that satisfy the system of equations are k = 2 and b = 2.8.

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.

CodeLlama 7B:

      To solve this system of linear equations, we can add the two equations to get:

    84m - 55s = 1 + 63m - 2s = 101

    This gives us:

    79m = 101

    Now, we can divide both sides by 79 to get:

    m = 101/79

    Similarly, we can solve the second equation to get:

    s = 98/2

    Therefore, the values of m and s are:

    m = 101/79
    s = 98/2

    So, the values of m and s are 101/79 and 98/2, respectively.

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.

CodeLlama 7B:

      To solve this system of equations, we need to follow the following steps:

    1. Subtract equation 2 from equation 1 to eliminate the variable b:

    (6 * b) + (5 * k) = 105
    (95 * k) - (51 * b) = 67

    Subtracting equation 2 from equation 1 gives us:

    (6 * b) + (5 * k) - (95 * k) + (51 * b) = 67 - 105

    This simplifies to:

    (-30 * k) + (51 * b) = -38

    2. Divide both sides of the equation by -30 to eliminate the variable k:

    (51 * b) / -30 = -1

    Multiplying both sides by -30 gives us:

    (51 * b) = 30

    3. Now, we can solve for b:

    b = 51 / 30
    b = 1

    Therefore, the value of b is 1.

    4. Now, we can substitute the value of b into equation 2 to solve for k:

    (95 * k) - (51 * 1) = 67

    Simplifying this equation gives us:

    95k - 51 = 67

    Dividing both sides by 51 gives us:

    k = 17

    Therefore, the values of b and k are b = 1 and k = 17.

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.

CodeLlama 7B:

      To solve this system of equations, we can add the two equations to get:

    33d + 62u = 114
    32u + 40d = 83

    Adding the two equations, we get:

    65d + 102u = 197

    Now, we can solve for d and u by dividing both sides of the equation by 65:

    d = 102u / 65
    u = 197 / 65

    Substituting the value of u into the first equation, we get:

    d = 102(197 / 65) / 65
    d = 102(3) / 65
    d = 306 / 65
    d = 5

    Substituting the value of d into the second equation, we get:

    u = 197 / 65
    u = 3

    Therefore, the values of d and u are 5 and 3, respectively.

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

CodeLlama 7B:

      Sure! To solve this system of equations, we can use substitution or elimination. Let's use substitution.

    We can solve the first equation for c:

    c = 102 / 5 - 28 / p

    Now, substitute this expression for c into the second equation:

    20 * (102 / 5 - 28 / p) - 67 * p = 13

    Expand and simplify:

    20 * 102 / 5 - 20 * 28 / p - 67 * p = 13

    Combine like terms:

    1020 - 560 - 67 * p = 13

    Subtract 67 * p from both sides:

    953 - 67 * p = 13

    Divide both sides by 67:

    p = 18

    Now that we have found p, we can substitute it back into the first equation to find c:

    c = 102 / 5 - 28 / 18

    c = 102 / 5 - 14 / 18

    c = 102 / 5 - 7 / 18

    c = 14

    So, the values of c and p are c = 14 and p = 18.

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.

CodeLlama 7B:

      To solve this system of linear equations, we can use substitution or elimination. Let's use substitution.

    We can solve the first equation for r:

    r = (147 - 12q) / 58

    Now, substitute this expression for r into the second equation:

    97q - 76(r/58) = 76

    Expand and simplify:

    97q - 76(147-12q)/58 = 76

    Now, we can solve for q:

    q = (76 + 76(147-12q)/58) / 97

    Simplify:

    q = (76 + 147q - 12q^2) / 97

    Now, we can solve for q:

    q^2 - 12q - 76 = 0

    Factor the left-hand side:

    (q - 6)(q - 13) = 0

    Solve for q:

    q = 6 or q = 13

    Now, we can find the value of r:

    r = (147 - 12q) / 58

    Substitute q = 6:

    r = (147 - 12(6)) / 58 = 12/58

    Substitute q = 13:

    r = (147 - 12(13)) / 58 = 11/58

    Therefore, the value of r is 12/58 and the value of q is 13.

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.

CodeLlama 7B:

      To solve this system of equations, we can first add the two equations to eliminate the k term:

    47 * v - 3 * k = 10
    73 * v + 2 * k = 128

    Adding the two equations, we get:

    110 * v = 138

    Now, we can divide both sides by 110 to solve for v:

    v = 138 / 110

    Now, we can substitute the value of v into one of the original equations to solve for k:

    47 * v - 3 * k = 10

    Substituting v = 138 / 110, we get:

    47 * (138 / 110) - 3 * k = 10

    Simplifying, we get:

    138 - 3 * k = 10

    Now, we can divide both sides by -3 to solve for k:

    k = -10 / 3

    So, the values of v and k are:

    v = 138 / 110
    k = -10 / 3

    Therefore, the system of equations has a unique solution, and the values of v and k are 138/110 and -10/3, respectively.

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?

CodeLlama 7B:

      To solve this system of equations, we need to solve the two equations simultaneously.

    First equation:
    89p - 41q = 60

    Second equation:
    27p + 91q = 124

    Now, we can add the two equations to get:

    89p - 41q = 60
    27p + 91q = 124

    Adding the two equations, we get:

    116p = 184

    Dividing both sides by 116, we get:

    p = 16

    Now, we can substitute the value of p in the first equation to get:

    89(16) - 41q = 60

    Substituting p = 16, we get:

    1272 - 41q = 60

    Now, we can divide both sides by -41 to get:

    q = -1272/41

    q = -30

    Therefore, the values of p and q are p = 16 and q = -30.

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

CodeLlama 7B:

      To solve these equations, we need to find the values of u and d that make them true.

    First, let's solve the first equation:

    (88 * u) - (96 * d) = 12

    We can simplify this equation by combining the like terms:

    88u - 96d = 12

    Now, we can solve for u and d:

    u = 12 / 88
    d = 12 / 96

    So, the values of u and d that make the first equation true are:

    u = 12 / 88 = 0.1379310345
    d = 12 / 96 = 0.1428571429

    Now, let's solve the second equation:

    (27 * u) + (36 * d) = 71

    We can simplify this equation by combining the like terms:

    27u + 36d = 71

    Now, we can solve for u and d:

    u = 71 / 27
    d = 71 / 36

    So, the values of u and d that make the second equation true are:

    u = 71 / 27 = 2.609677419
    d = 71 / 36 = 2.055555556

    Therefore, the values of u and d that make both equations true are:

    u = 0.1379310345
    d = 0.1428571429

    So, the values of u and d that make the equations true are:

    u = 0.1379310345
    d = 0.1428571429

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.

CodeLlama 7B:

      To solve this system of equations, we can first add the two equations to get:

    20n - 18f = 9 + 3n - 2f = 79

    This simplifies to:

    11n - 16f = 79

    Now, we can divide both sides by 11 to get:

    n = 79/11
    f = 79/16

    So, the values of f and n are:

    f = 79/16 = 5
    n = 79/11 = 7

    Therefore, the values of f and n are 5 and 7, respectively.

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.

CodeLlama 7B:

      To solve this system of equations, we can first add the two equations to eliminate the variable l:

    7 * l + 97 * j = 133
    22 * j + 37 * l = 76

    Adding the two equations, we get:

    97 * j = 133 + 76
    97 * j = 209

    Now, we can divide both sides by 97 to solve for j:

    j = 209 / 97
    j = 2.16

    Now, we can substitute the value of j into one of the original equations to solve for l:

    7 * l + 97 * 2.16 = 133
    7 * l = 133 - 174
    7 * l = -41

    Now, we can divide both sides by 7 to solve for l:

    l = -41 / 7
    l = -5.71

    Therefore, the values of j and l are j = 2.16 and l = -5.71.

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.

CodeLlama 7B:

      To solve this system of equations, we can add the two equations to get:

    21d - 46f = 53
    8d + 84f = 133

    Adding the two equations, we get:

    21d - 46f = 53
    8d + 84f = 133

    21d - 46f + 8d + 84f = 133 + 53

    21d + 84f = 186

    Now, we can solve for d and f by dividing both sides of the equation by 21:

    d + f = 186/21

    d + f = 9

    Now, we can solve for d and f by dividing both sides of the equation by 84:

    d + f = 9/84

    d + f = 0.1125

    Now, we can solve for d and f by rounding the answer to the nearest integer:

    d = 1
    f = -1

    Therefore, the values of d and f are 1 and -1, respectively.

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.

CodeLlama 7B:

      To solve this system of equations, we need to find the values of u and w that satisfy both equations.

    First, let's solve the first equation for u:

    u = 116 - 11w

    Now, substitute this expression for u into the second equation:

    66(116 - 11w) - 68w = 21

    Expand and simplify:

    66116 - 6611w - 68w = 21

    Combine like terms:

    66116 - 68w - 6611w + 21 = 0

    Subtract 6611w from both sides:

    -68w - 21 = 0

    Divide both sides by -68:

    w = 3

    Now that we have found w, we can find u:

    u = 116 - 11w
    u = 116 - 11(3)
    u = 116 - 33
    u = 83

    Therefore, the values of u and w that satisfy the system of equations are u = 83 and w = 3.

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.

CodeLlama 7B:

      To solve this system of equations, we need to solve for both f and j simultaneously. We can do this by adding the two equations and then solving for f and j.

    Adding the two equations, we get:

    76 * f - 42 * j = 96
    47 * j + 34 * f = 136

    Adding the two equations, we get:

    76 * f - 42 * j + 47 * j + 34 * f = 96 + 136

    Combine like terms:

    120 * f = 222

    Now, divide both sides by 120 to solve for f:

    f = 222/120 = 1.8

    Now, substitute the value of f into one of the original equations to solve for j:

    76 * 1.8 - 42 * j = 96

    Subtract 42 from both sides:

    34 * j = 54

    Divide both sides by 34:

    j = 54/34 = 1.5

    So, the values of f and j that satisfy the system of equations are f = 1.8 and j = 1.5.

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.

CodeLlama 7B:

      To solve this system of equations, we can add the two equations to get:

    68u + 32e = 174
    63e - 69u = 1

    Adding the two equations, we get:

    131u + 91e = 175

    Now, we can solve for u and e by subtracting the first equation from the second equation and dividing by 91:

    u = (175 - 131) / 91
    u = 44 / 91
    u = 0.476190476190476

    e = (175 - 131u) / 91
    e = (175 - 44) / 91
    e = 131 / 91
    e = 1.42857142857143

    Therefore, the values of u and e are 0.476190476190476 and 1.42857142857143, respectively.

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.

CodeLlama 7B:

      To solve this system of linear equations, we can add the two equations to get:

    57p + 4n = 129
    24p + 39n = 154

    Adding the two equations, we get:

    81p + 83n = 283

    Now, we can subtract 283 from both sides of the equation to get:

    -142p - 83n = -283

    Now, we can divide both sides of the equation by -142 to get:

    p/142 = -n/83

    Now, we can multiply both sides of the equation by 142 to get:

    p = -142n

    Now, we can substitute this value of p into one of the original equations to solve for n. For example, we can substitute p = -142n into the first equation to get:

    -142n + 4n = 129

    Now, we can simplify the equation by combining the like terms to get:

    -108n + 4n = 129

    Now, we can simplify the equation further by combining the like terms to get:

    -104n = 129

    Now, we can divide both sides of the equation by -104 to get:

    n = -129/104

    Now, we can substitute this value of n into the second equation to solve for p. For example, we can substitute n = -129/104 into the second equation to get:

    24(-129/104) + 39(-129/104) = 154

    Now, we can simplify the equation by combining the like terms to get:

    -3249/104 + -467/104 = 154

    Now, we can simplify the equation further by combining the like terms to get:

    -3716/104 = 154

    Now, we can divide both sides of the equation by -3716 to get:

    104/3716 = 154

    Now, we can simplify the equation further by combining the like terms to get:

    1/3716 = 154

    Now, we can divide both sides of the equation by 1/3716 to get:

    3716 = 154

    Now, we can simplify the equation further by combining the like terms to get:

    3716 = 154

    Now, we can solve for p by substituting this value of n into the first equation to get:

    57(-129/104) + 4(-129/104) = 129

    Now, we can simplify the equation by combining the like terms to get:

    -6539/104 + -504/104 = 129

    Now, we can simplify the equation further by combining the like terms to get:

    -6043/104 = 129

    Now, we can divide both sides of the equation by -6043 to get:

    104/6043 = 129

    Now, we can simplify the equation further by combining the like terms to get:

    1/6043 = 129

    Now, we can divide both sides of the equation by 1/6043 to get:

    6043 = 129

    Now, we can simplify the equation further by combining the like terms to get:

    6043 = 129

    Now, we can solve for p by substituting this value of n into the first equation to get:

    57(-129/104) + 4(-129/104) = 129

    Now, we can simplify the equation by combining the like terms to get:

    -6539/104 + -504/104 = 129

    Now, we can simplify the equation further by combining the like terms to get:

    -6043/104 = 129

    Now, we can

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.

CodeLlama 7B:

      To solve this system of equations, we can first add the two equations to eliminate the variable y:

    66 * z - 44 * y = 32
    60 * y + 14 * z = 116

    66 * z - 44 * y + 60 * y + 14 * z = 32 + 116

    100 * z = 150

    z = 150/100 = 1.5

    Now we can substitute the value of z into one of the original equations to solve for y:

    66 * 1.5 - 44 * y = 32

    66 - 44 * y = 32

    44 * y = 32 - 66

    y = (32 - 66) / 44

    y = -22 / 44

    y = -0.49

    So, the values of y and z are:

    y = -0.49
    z = 1.5

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.

CodeLlama 7B:

      To solve this system of equations, we can first add the two equations to eliminate the variable h:

    83t - 58h = 45
    69h + 11t = 124

    Adding the two equations, we get:

    83t - 58h + 69h + 11t = 124 + 45
    142t = 169

    Now, dividing both sides by 142, we get:

    t = 169/142

    Now, we can substitute this value of t into the first equation to find the value of h:

    83(169/142) - 58h = 45
    83/142 - 58h = 45/142
    -58h = 45/142 - 83/142
    -58h = -137/142
    h = 137/142

    Therefore, the values of t and h are:
    t = 169/142
    h = 137/142

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?

CodeLlama 7B:

      To solve this system of equations, we can add the two equations to get:

    (79 * h) - (61 * o) + (16 * h) - (12 * o) = 9 + 9

    Simplifying the equation, we get:

    (79 * h) - (61 * o) + (16 * h) - (12 * o) = 18

    Now, we can solve for h and o by dividing both sides of the equation by 18:

    h = (79 * o) / 18
    h = (16 * o) / 18

    Now, we can solve for o by subtracting the two equations:

    o = (79 * o) / 18 - (16 * o) / 18

    Simplifying the equation, we get:

    o = (53 * o) / 18

    Now, we can solve for o by dividing both sides of the equation by 53:

    o = 1 / 18

    Now, we can solve for h by substituting the value of o into one of the equations:

    h = (79 * o) / 18
    h = (16 * o) / 18

    Now, we can solve for h by substituting the value of o into one of the equations:

    h = (79 * 1 / 18)
    h = (16 * 1 / 18)

    Now, we can simplify the equations:

    h = 79 / 18
    h = 16 / 18

    Now, we can solve for h by dividing both sides of the equation by 18:

    h = 79 / 18 / 18
    h = 16 / 18 / 18

    Now, we can simplify the equations:

    h = 79 / 18
    h = 16 / 18

    Now, we can solve for h by dividing both sides of the equation by 18:

    h = 79 / 18
    h = 16 / 18

    Now, we can simplify the equations:

    h = 5
    h = 1

    Now, we can solve for h by adding the two equations:

    h = 5 + 1
    h = 6

    Now, we can solve for o by substituting the value of h into one of the equations:

    o = (79 * o) / 18
    o = (16 * o) / 18

    Now, we can solve for o by substituting the value of h into one of the equations:

    o = (79 * 1 / 18)
    o = (16 * 1 / 18)

    Now, we can simplify the equations:

    o = 1 / 18
    o = 1 / 18

    Now, we can solve for o by dividing both sides of the equation by 18:

    o = 1 / 18
    o = 1 / 18

    Now, we can simplify the equations:

    o = 1 / 18
    o = 1 / 18

    Now, we can solve for o by adding the two equations:

    o = 1 / 18 + 1 / 18
    o = 2 / 18

    Now, we can solve for o by dividing both sides of the equation by 2:

    o = 2 / 18
    o = 1

    Now, we can solve for h by substituting the value of o into one of the equations:

    h = (79 * o) / 18
    h = (16 * o) / 18

    Now, we can solve for h by substituting the value of o into one of the equations:

    h = (79 * 1) / 18
    h = (16 * 1) / 18

    Now, we can simplify the equations:

    h = 79 / 18
    h = 16 / 18

    Now, we can solve for h by dividing both sides of the equation by 18:

    h = 79 / 18
    h =

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

CodeLlama 7B:

      To solve for variables s and y in the system of equations, we can first combine like terms:

    4y + 56s = 139
    65y - 90s = 16

    Next, we can subtract the second equation from the first equation:

    4y + 56s - 65y + 90s = 139 - 16

    This simplifies to:

    -11y + 34s = 123

    Now, we can divide both sides of the equation by -11 to solve for s:

    s = -11/34 \* 123
    s = -3

    Now, we can substitute the value of s into one of the original equations to solve for y:

    4y + 56(-3) = 139
    4y + 174 = 139

    Subtracting 4y from both sides gives us:

    174 = 139

    Dividing both sides by 174 gives us:

    y = 139/174
    y = 0.79

    Therefore, the values of s and y are:

    s = -3
    y = 0.79

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.

CodeLlama 7B:

      To solve this pair of simultaneous equations, we can first add the two equations to eliminate the z term:

    42 * d - 4 * z = 75
    40 * d + 45 * z = 162

    42 * d - 4 * z + 40 * d + 45 * z = 75 + 162

    84 * d = 207

    d = 207 / 84
    d = 2.4

    Now, we can substitute the value of d into one of the original equations to find the value of z:

    42 * 2.4 - 4 * z = 75

    104.8 - 4 * z = 75

    z = 75 / 4 - 104.8
    z = 17.2

    Therefore, the values of d and z are:

    d = 2.4
    z = 17.2

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.

CodeLlama 7B:

      To solve this system of equations, we need to solve for both 'a' and 'o' simultaneously. We can do this by subtracting the second equation from the first equation and then solving for 'o'.

    (42 * o) + (24 * a) = 142
    (42 * a) + (6 * o) = 75

    Subtracting the second equation from the first equation, we get:

    (42 * o) + (24 * a) - (42 * a) - (6 * o) = 142 - 75

    This simplifies to:

    (24 * a) - (6 * o) = 67

    Now, we can solve for 'o' by dividing both sides of the equation by 24:

    o = 67/24

    o = 3

    Now, we can substitute the value of 'o' into the first equation to solve for 'a':

    (42 * 3) + (24 * a) = 142

    This simplifies to:

    126 + (24 * a) = 142

    Subtracting 126 from both sides of the equation, we get:

    24 * a = 17

    Dividing both sides of the equation by 24, we get:

    a = 17/24

    a = 0.75

    Therefore, the values of 'a' and 'o' are:

    a = 0.75
    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.

CodeLlama 7B:

      To solve this system of equations, we can first add the two equations to eliminate the variable r:

    39*r - 2*p = 45
    16*p - 84*r = 36

    Adding the two equations, we get:

    39*r - 2*p = 45
    16*p - 84*r = 36

    Adding the two equations, we get:

    39*r - 2*p + 16*p - 84*r = 45 + 36

    Combine like terms:

    55*p - 110*r = 81

    Now, we can solve for p and r:

    p = 81/55
    r = 81/110

    So, the values of p and r are:

    p = 1.53
    r = 0.70

    Therefore, the values of p and r are 1.53 and 0.70, respectively.

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

CodeLlama 7B:

      To solve this system of equations, we can first add the two equations to get:

    (23 * d) - (52 * w) + (64 * w) - (8 * d) = 7 + 58

    This simplifies to:

    (87 * d) - (130 * w) = 85

    Now, we can divide both sides of the equation by 87 to get:

    d - (130 * w) / 87 = 85 / 87

    Now, we can simplify the left-hand side of the equation by multiplying both sides by 87:

    d - w = 11

    Now, we can solve for 'd' by subtracting 'w' from both sides of the equation:

    d = 11 + w

    Now, we can substitute the expression for 'd' into the first equation:

    (23 * (11 + w)) - (52 * w) = 7

    This simplifies to:

    (23 * 11) - (52 * w) + (23 * w) = 7

    This simplifies to:

    263 - 114w + 23w = 7

    This simplifies to:

    150 - 114w = 7

    Now, we can solve for 'w' by subtracting 7 from both sides of the equation:

    143 - 114w = 0

    This simplifies to:

    29 - 114w = 0

    Now, we can divide both sides of the equation by 29 to get:

    -114w = 0

    Now, we can divide both sides of the equation by -114 to get:

    w = 0

    Now, we can substitute the expression for 'w' into the first equation:

    (23 * 11) - (52 * 0) = 7

    This simplifies to:

    263 - 52 = 211

    Now, we can solve for 'd' by substituting the expression for 'w' into the second equation:

    (64 * 0) - (8 * 11) = 58

    This simplifies to:

    0 - 88 = -88

    Now, we can solve for 'd' by adding 88 to both sides of the equation:

    -88 + 88 = 0

    Now, we can divide both sides of the equation by 88 to get:

    1 - 1 = 0

    Now, we can solve for 'd' by subtracting 1 from both sides of the equation:

    0 - 1 = -1

    Now, we can substitute the expression for 'd' into the first equation:

    (23 * (-1)) - (52 * 0) = 7

    This simplifies to:

    -263 - 0 = -263

    Now, we can solve for 'w' by substituting the expression for 'd' into the second equation:

    (64 * 0) - (8 * (-1)) = 58

    This simplifies to:

    0 - 8 = -8

    Now, we can solve for 'w' by adding 8 to both sides of the equation:

    -8 + 8 = 0

    Now, we can divide both sides of the equation by 8 to get:

    -1 + 1 = 0

    Now, we can solve for 'w' by subtracting 1 from both sides of the equation:

    0 - 1 = -1

    Now, we can substitute the expression for 'w' into the first equation:

    (23 * (-1)) - (52 * -1) = 7

    This simplifies to:

    -263 - 52 = -315

    Now, we can solve for 'd' by substituting the expression for 'w' into the second equation:

    (64 * -1) - (8 * (-1)) = 58

    This simplifies to:

    -64 - 8 = -72

    Now, we can solve for 'd' by adding 72 to both sides of

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.

CodeLlama 7B:

      To solve this system of equations, we can first add the two equations to get:

    (71 * z) + (60 * n) + (52 * z) - (47 * n) = 184 + 19

    This simplifies to:

    123 * z + 107 * n = 383

    Next, we can subtract 107n from both sides to get:

    123 * z = 383 - 107 * n

    Now, we can divide both sides by 123 to solve for n:

    n = (383 - 107 * n) / 123

    This is a recursive formula, which we can solve by starting with an initial value of n = 0 and iteratively substituting the previous value of n into the formula to find the next value.

    For example, if we start with n = 0, we get:

    n = (383 - 107 * 0) / 123 = 383 / 123 = 3

    So, the first value of n is 3. If we substitute this value into the formula, we get:

    n = (383 - 107 * 3) / 123 = 383 - 359 = 124 / 123 = 1

    So, the second value of n is 1. If we continue this process, we get:

    n = (383 - 107 * 1) / 123 = 383 - 107 = 276 / 123 = 2

    n = (383 - 107 * 2) / 123 = 383 - 214 = 170 / 123 = 1

    n = (383 - 107 * 1) / 123 = 383 - 107 = 276 / 123 = 2

    n = (383 - 107 * 2) / 123 = 383 - 214 = 170 / 123 = 1

    n = (383 - 107 * 3) / 123 = 383 - 359 = 124 / 123 = 1

    n = (383 - 107 * 4) / 123 = 383 - 426 = -93 / 123 = -0.77

    n = (383 - 107 * 5) / 123 = 383 - 549 = -166 / 123 = -1.31

    n = (383 - 107 * 6) / 123 = 383 - 676 = -293 / 123 = -2.23

    n = (383 - 107 * 7) / 123 = 383 - 803 = -470 / 123 = -3.64

    n = (383 - 107 * 8) / 123 = 383 - 930 = -507 / 123 = -4.07

    n = (383 - 107 * 9) / 123 = 383 - 1060 = -567 / 123 = -4.61

    n = (383 - 107 * 10) / 123 = 383 - 1157 = -694 / 123 = -5.69

    n = (383 - 107 * 11) / 123 = 383 - 1254 = -841 / 123 = -6.94

    n = (383 - 107 * 12) / 123 = 383 - 1351 = -988 /

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

CodeLlama 7B:

      To solve this system of equations, we can first add the two equations to eliminate the e term:

    70 + 99 = 169
    90 - 84 = 16

    Now, we can divide both sides of the first equation by 70 to get:

    e + z = 2.5

    Substituting this expression into the second equation, we get:

    99z - 84(2.5) = 20

    Simplifying, we get:

    99z - 202.5 = 20

    Now, we can divide both sides of the equation by 99 to get:

    z - 2.025 = 0.02

    Solving for z, we get:

    z = 2.025

    Now, we can substitute the value of z back into the first equation to get:

    e + 2.025 = 2.5

    Subtracting 2.025 from both sides, we get:

    e = 0.475

    Therefore, the values of e and z are:

    e = 0.475
    z = 2.025

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.

CodeLlama 7B:

      To solve this system of equations, we need to find the values of o and f that satisfy both equations.

    First, let's solve the first equation for o:

    26o - 44f = 95

    We can add 44f to both sides of the equation:

    26o = 95 + 44f

    Now, we can solve for o:

    o = (95 + 44f) / 26

    Now, let's substitute the expression for o into the second equation:

    87f + (95 + 44f) / 26 = 169

    Expanding the left-hand side of the equation, we get:

    87f + 95 + 44f = 169

    Combine like terms:

    142f = 84

    Now, divide both sides of the equation by 142 to solve for f:

    f = 84 / 142

    f = 0.625

    Now, substitute the value of f into the first equation to solve for o:

    o = (95 + 44(0.625)) / 26

    o = 95 + 44(0.625) / 26

    o = 95 + 18 / 26

    o = 95 + 0.68

    o = 103.68

    So, the values of o and f that satisfy the system of equations are o = 103.68 and f = 0.625.

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.

CodeLlama 7B:

      To solve this system of equations, we need to solve for both z and p. We can do this by using substitution or elimination.

    Let's use substitution. We can solve the first equation for z:

    z = 51/40

    Now, substitute this expression for z into the second equation:

    6(51/40) + 58p = 165

    Expand and simplify:

    6/40 + 58p = 165

    Now, solve for p:

    p = (165 - 6/40) / 58

    p = 27

    Now, substitute this value for p into the first equation:

    z = 51/40

    Now, solve for z:

    z = 51 - 20p

    z = 51 - 20(27)

    z = 51 - 570

    z = -565

    So, the values of z and p are:

    z = -565
    p = 27

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.

CodeLlama 7B:

      To solve this system of equations, we can first add the two equations to get:

    (71 * s) - (89 * f) + (3 * f) + (10 * s) = 5 + 93

    This simplifies to:

    (71 * s) + (10 * s) = 108

    Now, we can divide both sides of the equation by 10 to get:

    s = 108/10 = 10

    Now, we can substitute the value of s into the first equation to get:

    (71 * 10) - (89 * f) = 5

    This simplifies to:

    710 - 89f = 5

    Now, we can divide both sides of the equation by 89 to get:

    f = (710 - 5) / 89

    f = 705 / 89

    f = 8

    Therefore, the values of s and f are:

    s = 10
    f = 8

Expected answer: {f: 6553/1103, s: 8292/1103}

Correct? No