Answer:
Mother's present age: 42
Son's present age: 7
Step-by-step 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.
