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## Ratio problem

tagged by: rolandprowess

This topic has 1 expert reply and 3 member replies
gmatme Junior | Next Rank: 30 Posts
Joined
06 Mar 2007
Posted:
18 messages

#### Ratio problem

Sun Mar 18, 2007 8:39 am
The number of stamps that kaye and Alberto had were in the ratio 5:3 respectively. Afer Kaye gave Alberto 10 of her stamps, the ratio of the number of kaye had to the number Alberto had was 7:5. As a result of this gift, kaye had how many more stamps than Alberto?

a) 20
b) 30
c) 40
d) 60
e) 90

Ans given => C

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

Solving these 2 eq, got K = 175 and A = 105. So, Kaye had 70 more stamps than Alberto? Am i missing something here?

### GMAT/MBA Expert

Brent@GMATPrepNow GMAT Instructor
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GMAT Score:
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Sun Nov 05, 2017 3:46 pm
Quote:
The number of stamps that Kaye and Alberto had were in the ratio 5 : 3, respectively. After Kaye gave Alberto 10 of her stamps,the ratio of the number Kaye had to the number Alberto had was 7 : 5. As a result of this gift, Kaye had how many more stamps than Alberto?
A. 20
B. 30
C. 40
D. 6O
E. 9O
Let K = # of stamps K had after the exchange
Let A = # of stamps A had after the exchange
This means that K+10 = # of stamps K had before the exchange
This means that A-10 = # of stamps A had before the exchange

Note: Our goal is to find the value of K-A

The number of stamps that K and A (originally) had were in the ratio 5:3
So, (K+10)/(A-10) = 5/3
We want a prettier equation, so let's cross multiply to get 3(K+10) = 5(A-10)
Expand: 3K + 30 = 5A - 50
Rearrange: 3K - 5A = -80

After K gave A 10 of her stamps, the ratio of the number K had to the number A had was 7:5
So, K/A = 7/5
We want a prettier equation, so let's cross multiply to get 5K = 7A
Rearrange to get: 5K - 7A = 0

At this point we have two equations:
5K - 7A = 0
3K - 5A = -80

Our goal is to find the value of K - A.
IMPORTANT: We need not solve for the individual values of K and A. This is great, because something nice happens when we subtract the blue equation from the red equation.
We get: 2K - 2A = 80
Now divide both sides by 2 to get: K - A = 40

Cheers,
Brent

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### Top Member

Roland2rule Legendary Member
Joined
30 Aug 2017
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Sat Nov 04, 2017 11:55 pm
let the number of stamps Kaye and Alberto have to be x and y respectively.
At first, x:y = 5:3
or $$\frac{x}{y}=\frac{5}{3}$$
5y=3x or 3x-5y=0 ------(i)
As a result of the gift, Kaye now has (x-10) stamps and Alberto have (y+10) stamps, and the ratio is x-10: y+10=7:5
or $$\frac{x-10}{y+10}=\frac{7}{5}$$
5(x-10)= 7(y+10)
5x - 50= 7y +70
5x-7y= 120--------(ii)
solving the equations, we got the simultaneously
3x-5y=0
5x-7y= 120
solving this simultaneously, we get x=150 and y=90.
As a result of the gift , Kaye has (150-10) stamps, which equals 140. Alberto have (90+10=100) stamps.

the ratio of their number of stamps will be = 140:100
=14:10
=7:5
which means we are correct
Therefore, As a result of the gift, Kaye have (140-100=40) stamps more than Alberto.

jayhawk2001 Community Manager
Joined
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Sun Mar 18, 2007 8:46 am
Not sure how you got k = 175. The equations you have are spot on.

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

5k - 50 = 7A + 70
5*(5/3)*A - 50 = 7A + 70

25A - 150 = 21A + 210
4A = 360
A = 90
So K = 150

After the gift K has 140 and A has 100. So, difference = 40

gmatme Junior | Next Rank: 30 Posts
Joined
06 Mar 2007
Posted:
18 messages
Sun Mar 18, 2007 8:50 am

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