Gail's free-throw % is .875. How many free-throws has Gail made this year?

Question

She makes 13 out 20 of her next free-throws and her % drops to .860.

Answer 1

x/y = .875 x = .875y
(x + 13)/(y + 20) = .86
x + 13 = .86y + 17.2
x = .86y + 4.2 = .875y
so 4.2 = .015y
420 = 1.5 y
y = 280

280 before the 20; 300 after.

Answer 2

So, let X be the number of free-throws she made so far this year. Let N be the total number so far.

Thus, you know that: X/N = 0.875 which implies X = 0.875*N
And (X+13)/(N+20) = 0.86 which implies X + 13 = (N+20)*(0.86)

You can then solve this system of equations easily.