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Anna and Carol buy CDs and tapes at a music

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

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New post 11 Jul 2014, 05:37
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Difficulty:

  35% (medium)

Question Stats:

74% (01:55) correct 26% (02:18) wrong based on 176 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
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Re: Anna and Carol buy CDs and tapes at a music  [#permalink]

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New post 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

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

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New post 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

answer is A.
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Re: Anna and Carol buy CDs and tapes at a music  [#permalink]

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New post 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

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

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New post 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

Final Answer:

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

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New post 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

Answer (A)
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Re: Anna and Carol buy CDs and tapes at a music &nbs [#permalink] 16 Oct 2018, 00:12
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