Stamps

Let us assume that now Kaye has 7x stamps and Alberto has 5x stamps.
Hence, Kaye has 2x stamps more than Alberto.

Before the gift, Kaye had (7x + 10) stamps and Alberto had (5x - 10) stamps.
So, (7x + 10)/(5x - 10) = 5/3
--> 3(7x + 10) = 5(5x - 10)
--> (21x + 30) = (25x - 50)
--> 4x = 80
--> 2x = 40

The correct answer is C.

paresh_patil wrote:The number of stamps that K and A had were in the ratio 5:3, respectively. After K gave A 10 of her stamps, the ratio of the number K had to the number A had was 7:5. As a result of this gift, K had how many more stamps than A?
A) 20
B) 30
C) 40
D) 60
E) 90

We can also solve the question using 2 variables.
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