Retrospective Ages

Algebra Level 2

In another 8 years, Marvin will be twice as old as Kylene.
Ten years ago, the sum of their ages was 21.
How old will Marvin be in 20 years from now?

1 solution

A Former Brilliant Member
Oct 25, 2016

let $M$ be the age of Marvin now and $K$ be the age of Kylene now

In 8 years, the equation is

$M+8=2(K+8)$ $\implies$ $\boxed{M=2K+8}$ $\color{#D61F06}(1)$

10 years ago, the equation is

$(M-10)+(K-10)=21$ $\implies$ $\boxed{M+K=41}$ $\color{#D61F06}(2)$

Substitute $\color{#D61F06}(1)$ in $\color{#D61F06}(2)$

$2K+8+K=41$

$3K=33$

$K=11$

It follows that,

$M=2\times11+8$

$M=30$

Finally, after 20 years, the age of Marvin is

$M=30+20=50$