Tony is 21 years older than his sister Danielle. In 13 years he will be twice as old as Danielle. How old is each of them now?

x-y=21 ⇒ x=y+21

x+13=2y

Substitute y+21 for x into the equation x+13=2y

So y+21+13=2y

Simplify 34=y

So Danielle is 34 years old. Plug y back in to the original equation

x-34=21

x=55

Tony is 55 years old