Question

A mother is currently 7 times older than her son. In 3 years time, she will be 5 times older than her son. Let x and y be the present ages of the son and mother respectively.

Answer 1

If the child is currently 6 years old and the mom is 42, in three years she'll be 45 and he'll be 9

Explanation:

The son is y and the mom is x

x=7y

x+3=5(y+3)

7y+3=5y+15

7y=5y+12

2y=12

y=6

Answer 2

Mother's present age: 42

Son's present age: 7

Explanation:

Let x represent the mother's age

Let y represent the son's age

The mother is currently seven times (×7) older than her son i.e.

x = 7 × y

x = 7y .............. (eqn 1)

In three years time i.e. the mother and son's age plus three (3)

x + 3 and y + 3

The mother will be 5 times (×5) older i.e.

x + 3 = 5 × (y + 3)

x + 3 = 5(y + 3)

x + 3 = 5y + 15

Collect like terms

x = 5y + 12 ........... (eqn 2)

Since x = 7y in eqn 1, we substitute x in eqn 2 i.e.

7y = 5y + 12

7y - 5y = 12

2y = 12

y = 6

Since y=6, we substitute 6 in eqn 1

x = 7y

x = 7 × 6

x = 42

Hence, the present age of the mother and her son are 42 and 6 respectively.