On chris' birthday in 1992, he was half the age of his brother joseph. on chris' birthday in 1998, he was two-thirds the age of joseph. how old will chris be on his birthday in 2018?

On Chris' birthday in 1992, he was half the age of his brother Joseph. On Chris' birthday in 1998, he was two-thirds the age of Joseph. How old will Chris be on his birthday in 2018?

Step 1: Form an equation. 
We know that in 1992, Chris was HALF the age of Joseph. So Chris was x years old, while his brother was twice his age, or 2x. 6 years later, he was two-thirds the age of his brother. So, he was (x+6) while his brother was (2x+6).

So, we can form this:

(X+6)=(2/3)(2x+6)

Step 2: Simplify the equation. Distribute, Subtract, multiply

(X+6)=(2/3)(2x+6)
Distribute: X+6=(2/3)(2x)+(2/3)(6)
X+6=4/3x+4

Subtract:
X+6-4/3x=4/3x+4-4/3x
-1/3x+6=4

Subtract:
-1/3x+6-6=4-6
1/3x=-2

Multiply:
(3/-1) * (-1/3x)=(3/-1)*(-2)

X=6

This means in 1992, Chris was indeed 6 years old, while his brother was 12. 6 years later, Chris was 12 years old, while his brother was 18. (6/12=1/2; 12/18=2/3)

So, from 1992-2018=26 years.

In 1992 Chris was already 6.
26+6=32

In 2018, Chris is 32 years old, his brother is 6 years older, 38.

Chris is 32 years old.

~Hope this helps!