Question

Joan is 5 years older than Ellen, and 3 years ago the sum of their ages was 17 years. In how many years will Joan be 21 years old?

Answer 1

7

Explanation:

If J is Joan's current age and E is Ellen's current age, then:

J = E + 5

(J - 3) + (E - 3) = 17

Solve the first equation for E:

E = J - 5

Substitute into the second:

(J - 3) + (J - 5 - 3) = 17

J - 3 + J - 8 = 17

2J - 11 = 17

2J = 28

J = 14

Joan is 14, so in 7 years, she will be 21.