let

x = the present age of Peter

y = the present age of Mary

Peter is 15 years older than Mary

x = 15 + y

5 years later he will be twice as old as Mary

x + 5 = 2(y + 5)

by solving the system of equations

x = 15 + y

x + 5 = 2(y + 5)

we find

x = 25 years

y = 10 years

Peter is 25 years old now.

Mary is 10 years old now.