Question

Jack is 5 times younger than her mother. In 6 years, Jack will be three times younger than her mother. How old is each now?

Answer 1

Jack is 6 and Mom is 30

Explanation:

J = Jacks age

M = Mom's age

5J = M

In 6 years, so add 6 to the age

3(J+6) = (M+6)

We have a system of 2 equations and 2 unknowns

Lets simplify the 2nd equation

3(J+6) = (M+6)

3J + 18 = M+6

Substituting M =5J

3J + 18 = 5J +6

Subtract 3J from each side

3J-3J + 18 = 5J-3J +6

18 = 2J+6

Subtract 6 from each side

18-6 = 2J+6-6

12 = 2J

Divide each side by 2

12/2 = 2J/2

6=J

Jack is 6

We still need to find Mom's age

M = 5J

= 5*6

=30

Mom is 30