Family Math

A mother is four times as old as her son is now. In twenty years she will be only twice as old as her son. How old are the mother and son now?

This problem can be solved through algebraic thinking. Let's allow M to represent the mother's age and S represent her son's age.

"A mother is four times as old as her son is now."

M = 4S

"In twenty years, she will be only twice as old as her son."

M + 20 = 2(S + 20)

Algebraically, we can solve for S, arriving at the son's age now.

M + 20 = 2(S + 20)

M + 20 = 2S + 40

M = 2S + 20

By substituting 4S in for the value of M, we have:

4S = 2S + 20

2S = 20

S = 10

Therefore, the mother's age now is M = 4S = 4(10) = 40.

We can double check our answer by following the facts of the problem.

If the son is 10 years old and the mother is 40, then indeed the mother is 4 times as old as her son is now. In twenty years, th son will be 30 and the mother will be 60. Indeed, the mother will only be twice as old as her son.

 

Extension: Ask your students to think of their own "family's math." Encourage them to use whatever family members they want and to be as creative as they want.

Reference: Project INTERMATH

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