-- Let's call the age of the older brother ' A '.
-- Their ages are in the ratio of 2 to 3, so the age of the younger guy is (2/3 A).
-- In 8 years, their ages will be (A + 8) and (2/3 A + 8).
-- The ratio of their ages will be 3 to 4, so we can write
(2/3 A + 8) / (A+8) = 3/4 .
Multiply each side by (A + 8):
(2/3 A+8) = (3/4) (A + 8)
Eliminate the parentheses:
2/3 A + 8 = 3/4 A + 6
Subtract 2/3 A from each side:
8 = 1/12 A + 6
Subtract 6 from each side:
2 = 1/12 A
Multiply each side by 12:
24 = A
Check:
-- Their ages are in the ratio of 2:3 today ... they're 16 and 24
-- In 8 years, they'll be 24 and 32 .
-- The ratio of 24 to 32 is 3:4 . yay !
