Anna and Carol buy CDs and tapes at a music

Question

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

VladimirKarpov · Answer

CD => C
Type => T

Carol: 4C+5T=50
Anna: 12C+5T=100

12C-4C=50
8C=50
C=6.25

4C+5T=50
25+5T=50
5T=25
T=5

Answer is A

mvictor · Answer

C=50=4x+5y
A=2C=100=8x+10y
12x+5y=100=8x+10y
4x=5y

plugin first equation:
10y=50
y=5

answer is A.

JeffTargetTestPrep · Answer

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

EMPOWERgmatRichC · Answer

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

KarishmaB · Answer

Assuming cost of each CD is C and cost of each tape is T,

4C + 5T = 50 ... (I)
12C + 5T = 100 ... (II)

multiply (I) by 3 to get
12C + 15T = 150 ... (III)

(III) - (II), we get 10T = 50
T = $5

Answer (A)

Manasvi1 · Answer

Let C.P. of 1 CD be  x  and C.P. of 1 tape be  y 
Given, Anna spends twice than Carol and Carol spends $50

So, money spent by anna = $100
Anna buys 3 times Cd and same no.of tapes and carol buys 4 CDs and 5 tapes.

So,anna buys 12 CD and 5 tapes

Therefore,
12x + 5y = 100 .....1
4x + 5y = 50 .....2

Subtracting 2 from 1,we get
8x = 50 => x=50/8

From 2, 4x + 5y = 50
 => 25 + 5y = 50
 => 5y = 25
 => y = 25/5 = 5
So, C.P. of 1 tape is $5
 Therefore OA (A)

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

Anna and Carol buy CDs and tapes at a music

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

Anna and Carol buy CDs and tapes at a music

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards