Answer to Question #210820 in Algebra for ooo

Question

Currently, Nora is 3 times as old as Damon. In 8 years, she will only be 2 times as old as Damon. How old will Damon be in 8 years?

Answer 1

Let Nora be $x$ years old and let Damon be $y$ years old.

Nora is 3 times as old as Damon: $x=3y$ .

In 8 years, Nora will only be 2 times as old as Damon: $x+8=2(y+8)$

$\begin{cases} x=3y \\ x+8=2y+16 \end{cases}\qquad \begin{cases} x=3y \\ 3y+8=2y+16 \end{cases}\qquad \begin{cases} x=24 \\ y=8 \end{cases}$

Now Damon is $8$ years old. In $8$ years Damon’s age will be $8+8=16$ .

Answer: $16$ years.