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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by Gmat_mission » Tue Nov 10, 2020 7:47 am

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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

Source: Beat The GMAT — Problem Solving | Tue Nov 10, 2020 7:47 am

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Re: 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 tap

by Scott@TargetTestPrep » Mon Nov 16, 2020 12:32 pm

Gmat_mission wrote: ↑
Tue Nov 10, 2020 7:47 am
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

Solution:

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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