Four years ago, Danielle was 2/3 as old as Jim was. Now she is 3/4 as old as he is. How old is each now?

Answer 1

Jim's present age ---- x
Danielle's present age ----- 3x/4

4 years ago:
Jim ---- x-4
Danielle ----- 3x/4 - 4

3x/4 - 4 = (2/3)(x-4)
3x/4 - 4 = 2x/3 - 8/3
multiply each term by 12
9x - 48 = 8x - 32
x = 16

Jim is now 16, and Danielle now is 12

check:
4 years ago Jim was 12 and Danielle was 8
is 2/3 of 12 equal to 8? yes!

Answer 2

D - 4 = 2/3 (J - 4) ...3 D - 12 = 2 J - 8

D = 3/4 J

substituting ... 9/4 J = 8/4 J + 4

solve for J , then substitute back to find D