Jack is 4 times as old as Lacy. 3 years ago the sum of their ages was 64. How old are they now?

We can create a system of equations with the information we know.

J = 4L

J + L - 6 = 64

The first equation is pretty self-explanatory. Jack is 4 times as old as Lucy. The second equation is just adding their ages together. We subtract 6 because the sum of their ages was 64 three years ago. Three years ago, both Jack and Lucy were 3 years younger (total of 6).

Substitute 4L in for J in the second equation and solve.

4L + L - 6 = 64

5L = 70

L = 14

If Lucy is 14, then Jack is 14*4 = 56.