Question

Question #d3d11

Answer 1

The father is 24 years old, and the son is 6 years old.

Explanation:

Let x represent the son's age.
Let y represent the man's age.

Make two equations:

(1) The man's age is equal to four times his son's age:

`y = 4x`

(2) In three years the man's age will be `y + 3`.
In three years the son's age will be `x + 3`.
In three years the man's age will be equal to three times his son's age.

`y + 3 = 3 (x+3)`

Expand the second equation:

`y + 3 = 3 (x+3)`

`y + 3 = 3x+9`

Equate the two equations:

Since `y = 4x`, you can replace the `y` in the second equation with `4x`

`y + 3 = 3x+9`

`4x + 3 = 3x+9`

Simplify the equation:

`4x + 3 = 3x+9`

`4x-3x+3= 9`

`4x-3x=9-3`

`x=6`

Substitute this value into the first equation:

`y = 4x`

`y = 4(6)`

`y = 24`

Therefore the son's age `(x)` is 6 years and the man's age `(y)` is 24 years.