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
Brent Hanneson - Creator of GMATPrepNow.com
