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The number of stamps Kaye and Alberto had were in the ratio

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The number of stamps Kaye and Alberto had were in the ratio [#permalink]

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New post 29 Sep 2008, 06:19
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Question Stats:

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The number of stamps that Kaye and Alberto had were in the ration of 5:3 respectively. After Kaye gave Alberto 10 of her stamps, the ration of the number of Kaye had to the number of Alberto had was 7:5. As a result of the gift, Kaye had how many more stamps than Alberto?

A. 20
B. 30
C. 40
D. 60
E. 90

OPEN DISCUSSION OF THIS QUESTION IS HERE: the-number-of-stamps-that-kaye-and-alberto-had-were-in-the-98116.html
[Reveal] Spoiler: OA
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Re: The number of stamps Kaye and Alberto had were in the ratio [#permalink]

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pawan203 wrote:
The number of stamps Kaye and Alberto had were in the ratio 5:3 respectively. After Kaye gave Alberto 10 of her stamps, the ratio of the number of stamps Kaye had to the number Alberto had was 7:5. As a result of this gift Kaye had how many more stamps than Alberto?

(1) 20
(2) 30
(3) 40
(4) 60
(5) 90


C

K1 = 5x
A1 = 3x

K2 = 5x - 10
A2 = 3x + 10

K2/A2 = 7/5

(5x-10)/(3x+10) = 7/5
5*(5x-10) = 7*(3x+10)
25x - 50 = 21x + 70
4x = 120
x = 30

K2 = 5*30 - 10 = 140
A2 = 3*30 + 10 = 100

K2 - A2 = 40
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Re: The number of stamps Kaye and Alberto had were in the ratio [#permalink]

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New post 09 Nov 2011, 08:53
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Hi,

I was trying to set up two equations:

K/A = 5/3
(K-10) / (A+10) = 7/5

when solving, I got A = 90 and K = 150, so K-A = 60. Why is this approach wrong?
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Re: The number of stamps Kaye and Alberto had were in the ratio [#permalink]

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Re: The number of stamps Kaye and Alberto had were in the ratio [#permalink]

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New post 13 Oct 2014, 02:05
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The number of stamps that Kaye and Alberto had were in the ration of 5:3 respectively. After Kaye gave Alberto 10 of her stamps, the ration of the number of Kaye had to the number of Alberto had was 7:5. As a result of the gift, Kaye had how many more stamps than Alberto

A. 20
B. 30
C. 40
D. 60
E. 90

Given: \(\frac{K}{A}=\frac{5x}{3x}\) (where \(x\) is a positive integer) and \(\frac{5x-10}{3x+10}=\frac{7}{5}\) --> \(x=30\) --> \(K=150\) and \(A=90\).

Question: \((K-10)-(A+10)=?\) --> \((K-10)-(A+10)=40\).

Answer: C.

OPEN DISCUSSION OF THIS QUESTION IS HERE: the-number-of-stamps-that-kaye-and-alberto-had-were-in-the-98116.html
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Re: The number of stamps Kaye and Alberto had were in the ratio   [#permalink] 13 Oct 2014, 02:05
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