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. 60

E. 90

D.

Step-by-step explanation:

Let the number of stamps Kaye had be k and that of Alberto be a. Then we know that are in a ratio of 5 to 3.

Hence, k : a = 5:3

or 3k = 5a

Then Kaye gave Alberto 10 of her stamp to make the ratio 7:5

k - 10/a + 10 = 7/5

Cross multiply:

5 (k - 10) = 7 (a + 10)

5k - 50 = 7a + 70

5k - 7a = 120

Let us now solve the last equation simultaneously with the equation 3k = 5a

5k - 7a = 120

3k - 5a = 0

Multiply equation 1 by 3 and equation 2 by 5

15k - 21a = 360

15k - 25a = 0

Subtract 1 from 2, 4a = 360

and thus a = 90

We know 3k = 5a

3k = 5 * 90

k = 450/3 = 150

Now if we subtract 90 from 150, this yields 60