Please act as a match teacher, directly answer the question and give the explanation.
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# Question:
Two friends plan to walk along a 43-km trail, starting at opposite ends of the trail at the same time. If Friend P's rate is 15% faster than Friend Q's, how many kilometers will Friend P have walked when they pass each other?
# Options:
A)21
B)21.5
C)22
D)22.5
E)23
# Answer:
The answer is: E
# Explanation:
If Q complete x kilometers, then P completes 1.15x kilometers. x + 1.15x = 43. 2.15x=43. x = 43/2.15 = 20. Then P will have have walked 1.15*20=23 km.
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# Question:
In the coordinate plane, points (x, 1) and (5, y) are on line k. If line k passes through the origin and has slope 1/5, then what are the values of x and y respectively?
# Options:
A)4 and 1
B)1 and 5
C)5 and 1
D)3 and 5
E)5 and 3
# Answer:
The answer is: C
# Explanation:
Line k passes through the origin and has slope 1/5 means that its equation is y=1/5*x. Thus: (x, 1)=(5, 1) and (5, y) = (5,1) -->x=5 and y=1.
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# Question:
Carl is facing very difficult financial times and can only pay the interest on a $10,000 loan he has taken. The bank charges him a quarterly compound rate of 4%. What is the approximate interest he pays annually?
# Options:
A)$1600
B)$2000
C)$2150
D)$2500
E)$12000
# Answer:
The answer is: A
# Explanation:
Here you find per quarter rate as (16/4)% = 4%. So the bank charges 4% every quarter and compounds it in the next quarter. Had it been a simple quarterly rate, we would have just found 4 * 4% of 10,000 = $1600 as our answer. But since, the interest is compounded, it will be a bit more than $1600.
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# Question:
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# Options:
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# Answer:
