kilukilam
The number of stamps that Kaye and Alberto had were in the ration of 5:3 respecctively. 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
One option is to solve the question using TWO VARIABLES.
Let K = # of stamps K had
after the exchangeLet A = # of stamps A had
after the exchangeThis 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 5:3So, (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 = -80After K gave A 10 of her stamps, the ratio of the number K had to the number A had was 7:5So, K/A = 7/5
We want a prettier equation, so let's cross multiply to get 5K = 7A
Rearrange to get:
5K - 7A = 0At this point we have two equations:
5K - 7A = 03K - 5A = -80Our 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:
Cheers,
Brent