let

x = the age of Jane at the moment

y = the age of Luke at the moment

Jane is 3 times as old as Luke

x = 3y

10 ago, Jane was five times as old as Luke

x - 10 = 5(y - 10)

by solving the system of equations

x = 3y

x - 10 = 5(y - 10)

we find

x = 60 years

y = 20 years

Luke is 20 years old now.

Jane is 60 years old now.