x - Orville's age
y - Wilbur's age
Five years ago, Orville was twice as old as Wilbur.
[tex]x-5=2(y-5) \\
x-5=2y-10 \\
x=2y-10+5 \\
x=2y-5[/tex]
Five years from now, Orville will be one and one half times as old as Wilbur.
[tex]x+5=1 \frac{1}{2}(y+5) \\
x+5=\frac{3}{2}(y+5) \\
x+5=\frac{3}{2}y+\frac{15}{2} \\
x=\frac{3}{2}y+\frac{15}{2}-5[/tex]
Set both expressions equal to each other:
[tex]x=x \\
2y-5=\frac{3}{2}y+\frac{15}{2}-5 \ \ \ |+5 \\
2y=\frac{3}{2}y+\frac{15}{2} \ \ \ |\times 2 \\
4y=3y+15 \\
4y-3y=15 \\
y=15 \\ \\
x=2y-5=2 \times 15-5=30-5=25
[/tex]
Orville is 25 years old.
Wilbur is 15 years old.
