John is five years older than Jane. In three years, his age will be twice what her age will be. How old is each person?

Answer 1

Let John's age right now be J. His age in three years will be J+3

Let Jane's age right now be N. Her age in three years will be N+3

Right now, J = 5+N

In three years J+3 = 2(N+3)

Need to solve this system of equations. Can substitute "5+N" into any J and get

5+N + 3 = 2(N+3)

Distribute the 2 into the parentheses.

5+N + 3 = 2N + 6

Collect like terms

N + 8 =2N + 6

Subtract N from both sides.

8 = N + 6

Subtract 6 from both sides.

2 = N Jane is 2 years old. John is 7 years old.

(in 3 years Jane will be 5, John will be 10, and John will be twice as old as Jane - so our answer is correct.)