Problem Solving

Hi All,

We're told that 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, we're asked for the price of one tape cost. This question can be approached in a couple of different ways; since every approach requires that you translate the information into equations, you might find it easiest to approach this work Algebraically.

Since Carol spent $50 on 4 CDs and 5 tapes, we can create the following equation:
50 = 4C + 5T

We know that Anna spends TWICE as much as Carol, buying 3 times as many CDs and the same number of tapes. This can be translated into:
100 = 12C + 5T

Thus, the difference in the total spent comes down to the difference in the number of CDs purchased:
An extra 50 dollars gets you an extra 8 CDs
50 = 8C
50/8 = C
25/4 = C

We can now 'plug' this value into the first equation:
50 = (4)(25/4) + 5T
50 = 25 + 5T
25 = 5T
5 = T

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

BTGmoderatorDC wrote: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

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