On Chris's 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?

Suppose in 1992 Chris was x years old, his brother was then 2x years old.

6 years later in 1998, Chris is (x+6) years old, his brother is (2x+6),

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

x+6 = (4/3) x+4

(4/3) x-x=6-4

(1/3) x=3

x=6

in 1992, Chris was 6, so in 2018 he will be 6 + (2018-1992) = 32 years old.