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# Anna and Carol buy CDs and tapes at a music

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Manager
Joined: 04 Aug 2013
Posts: 96
Location: India
Schools: McCombs '17
GMAT 1: 670 Q47 V35
GPA: 3
WE: Manufacturing and Production (Pharmaceuticals and Biotech)

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11 Jul 2014, 05:37
2
1
00:00

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(N/A)

Question Stats:

77% (02:27) correct 23% (02:33) wrong based on 183 sessions

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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
Intern
Joined: 24 Apr 2013
Posts: 16
Location: Russian Federation
Re: Anna and Carol buy CDs and tapes at a music  [#permalink]

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11 Jul 2014, 05:54
3
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

Board of Directors
Joined: 17 Jul 2014
Posts: 2587
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
Re: Anna and Carol buy CDs and tapes at a music  [#permalink]

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10 Apr 2017, 13:08
anceer 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

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

plugin first equation:
10y=50
y=5

Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2827
Re: Anna and Carol buy CDs and tapes at a music  [#permalink]

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14 Jul 2018, 09:20
anceer 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

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Re: Anna and Carol buy CDs and tapes at a music  [#permalink]

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15 Oct 2018, 22:01
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

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Re: Anna and Carol buy CDs and tapes at a music  [#permalink]

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16 Oct 2018, 00:12
anceer 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

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

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Karishma
Veritas Prep GMAT Instructor

Re: Anna and Carol buy CDs and tapes at a music   [#permalink] 16 Oct 2018, 00:12
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