# A father is four times as old as his daughter. In 6 years, he will be three times as old as she is. How old is the daughter now?

Dec 28, 2016

The daughter is $12$ years old.

#### Explanation:

We shall consider the father´s age as $x$ and the daughter´s age as $y$. From the details, we can write these two equations:

$x = 4 y$
$x + 6 = 3 \left(y + 6\right)$

Simplify the second equation by opening the brackets.

$x + 6 = 3 y + 18$

Subtract $6$ from both sides.

$x = 3 y + 12$

Using the value of $x$ from the first equation, substitute $x$ in the simplified second equation with $\textcolor{red}{4 y}$.

$x = 3 y + 12$

$\textcolor{red}{4 y} = 3 y + 12$

Subtract $3 y$ from both sides.

$y = 12$