difference of ages

Algebra Level 1

The ratio of the age of $\text{B}$ to the age of $\text{A}$ is $\dfrac{1}{2}$ . Ten years from now, the age of $\text{B}$ will be $62.5\%$ of the age of $\text{A}$ at that time. What was the positive difference of their ages five years ago?

25 15 10 20

1 solution

A Former Brilliant Member
Apr 4, 2018

We have two equations,

$A=2B$ and $B+10=0.625(A+10)$

Solving these system of equations gives $A=30$ and $B=15$ . So five years ago, $A$ was 25 and $B$ was 10 and the difference of their ages was 25-10=15.

difference of ages

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