Question

Five years ago, Orville was twice as old as Wilbur. Five years from now, Orville will be one and one half times as old as Wilbur. How old is each now?

Answer 1

x - Orville's age
y - Wilbur's age

Five years ago, Orville was twice as old as Wilbur.

`x-5=2(y-5) \\ x-5=2y-10 \\ x=2y-10+5 \\ x=2y-5`

Five years from now, Orville will be one and one half times as old as Wilbur.

`x+5=1 (1)/(2)(y+5) \\ x+5=(3)/(2)(y+5) \\ x+5=(3)/(2)y+(15)/(2) \\ x=(3)/(2)y+(15)/(2)-5`

Set both expressions equal to each other:

`x=x \\ 2y-5=(3)/(2)y+(15)/(2)-5 \ \ \ |+5 \\ 2y=(3)/(2)y+(15)/(2) \ \ \ |* 2 \\ 4y=3y+15 \\ 4y-3y=15 \\ y=15 \\ \\ x=2y-5=2 * 15-5=30-5=25`

Orville is 25 years old.
Wilbur is 15 years old.