Ratio problem

[gmatme]

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?

[jayhawk2001]

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]

Silly addition.........! Thanks!

[BTGmoderatorRO]

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.

[Brent@GMATPrepNow]

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

Answer: C

Cheers,
Brent

[Scott@TargetTestPrep]

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

We are given that the number of stamps that Kaye and Alberto had was in the ratio 5 : 3. We can represent this as:

K : A = 5x : 3x

We are next given that after Kaye gave Alberto 10 of her stamps, the ratio of the number Kaye had to the number Alberto had was 7 : 5. Using this information, we can create the following equation:

(5x - 10)/(3x + 10) = 7/5

5(5x - 10) = 7(3x + 10)

25x - 50 = 21x + 70

4x = 120

x = 30

Kaye now has 5(30) - 10 = 140 stamps, and Alberto has 3(30) + 10 = 100 stamps. So Kaye has 140 - 100 = 40 more stamps than Alberto has.

Answer: C