let ben's current age be b and carol's current age be c

set up two equations

sum of their ages is 36, so:

b+c = 36

nine years ago ben was twice as old as carol:

(b-9) = 2(c-9)

solve for b in the first:

b = 36-c

substiute this into the second

(36-c-9) = 2(c-9)

27-c = 2c - 18

27 = 3c - 18

45 = 3c

15 = c

solve for b

b = 36 - c

b = 36 - 15

b = 21

so Ben is currently 21 years old and Carol is currently 15 years old.