The sum of the ages of Kristen and Ben is 32. Four years ago Kristen was twice as old as Ben. How old are they both now?

Let us say that:

K = age of Kristen

B = age of Ben

From the problem, we make the equations:

eqtn 1: K + B = 32

eqtn 2: (K - 4) = 2 (B - 4)

Simplifying eqtn 2:

K - 4 = 2 B - 8

K = 2 B - 4

Plugging in this to eqtn 2:

(2 B - 4) + B = 32

3 B - 4 = 32

3 B = 36

B = 12

From eqtn 2:

K = 2 B - 4 = 2 (12) - 4 = 20

So Kristen is 20 while Ben is 12.