Derek is four times as old as sarah. two years ago the sum of their ages was 36. how old is each now?

Let's write a system of equations. We will use D for Derek's age and S for Sarah's age:

D = 4S

(D - 2) + (S - 2) = 36

We can simplify the second equation:

D + S - 4 = 36

D + S = 40

Now we can use substitution to plug 4S in for D in the second equation:

(4S) + S = 40

5S = 40

S = 8

Sarah is 8 years old.