Math CentralQuandaries & Queries


Question from Heather:

My granddaughter had this third grade math problem. Aaron is 4 times as old as his brother Bill. In ten years Aaron will be twice Bills age. What are their ages?

Suppose Aaron is $A$ years old and Bill is $B$ years old. Since Aaron is 4 times as old as Bill

\[A = 4 \times B.\]

In 10 years how old will Aaron be? How old will Bill be? At this time Aaron will be twice as old as Bill. This gives you a second equation in $A$ and $B.$ Can you solve the pair of equations for $B?$

Make sure you verify your answer.

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