let

x = the age of Mike

y = the age of Mary

Mike is three times as old as his little sister Mary:

x = 3y

In 4 years, he will be twice as old as Mary:

x + 4 = 2y

by solving the system of equations:

x = 3y

x + 4 = 2(y + 4)

we find:

x = 12 years

y = 4 years

click here to see the step by step solution of the system of equations:

Click to see all the steps

Mary is 4 years old now.