Anna and Carol buy CDs and tapes at a music store that sells each of its CDs for a certain price and each of its tapes for a certain price. Anna spends twice as much as Carol spends, buying three times as many CDs and the same number of tapes. If Carol spends \(\$50.00\) on four CDs and five tapes, how much does one tape cost?
A \(\$5.00\)
B \(\$6.25\)
C \(\$12.00\)
D \(\$25.00\)
E \(\$100.00\)
Answer: A
Source: Princeton Review
Anna and Carol buy CDs and tapes at a music store that sells each of its CDs for a certain price and each of its tapes
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Solution:Gmat_mission wrote: ↑Tue Nov 10, 2020 7:47 amAnna and Carol buy CDs and tapes at a music store that sells each of its CDs for a certain price and each of its tapes for a certain price. Anna spends twice as much as Carol spends, buying three times as many CDs and the same number of tapes. If Carol spends \(\$50.00\) on four CDs and five tapes, how much does one tape cost?
A \(\$5.00\)
B \(\$6.25\)
C \(\$12.00\)
D \(\$25.00\)
E \(\$100.00\)
Answer: A
Let c denote the price of one CD and t denote the price of one tape (both in dollars).
We can create the following equation for Carol’s expenditure:
4c + 5t = 50
We can create the following equation for Anna’s expenditure:
12c + 5t = 100
Subtracting the first equation from the second, we have:
8c = 50
c = 50/8 = 6.25
Thus:
4(6.25) + 5t = 50
5t = 25
t = 5
Answer: A
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