# Question #d3d11

Aug 8, 2017

#### Answer:

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:

$y = 4 x$

(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.

$y + 3 = 3 \left(x + 3\right)$

Expand the second equation:

$y + 3 = 3 \left(x + 3\right)$

$y + 3 = 3 x + 9$

Equate the two equations:

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

$y + 3 = 3 x + 9$

$4 x + 3 = 3 x + 9$

Simplify the equation:

$4 x + 3 = 3 x + 9$

$4 x - 3 x + 3 = 9$

$4 x - 3 x = 9 - 3$

$x = 6$

Substitute this value into the first equation:

$y = 4 x$

$y = 4 \left(6\right)$

$y = 24$

Therefore the son's age $\left(x\right)$ is 6 years and the man's age $\left(y\right)$ is 24 years.