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?

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Answer 1 · 2016-12-28T04:29:28

The daughter is $12$ years old.

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:

$x=4y$
$x+6=3(y+6)$

Simplify the second equation by opening the brackets.

$x+6=3y+18$

Subtract $6$ from both sides.

$x=3y+12$

Using the value of $x$ from the first equation, substitute $x$ in the simplified second equation with $color(red)(4y)$ .

$x=3y+12$

$color(red)(4y)=3y+12$

Subtract $3y$ from both sides.

$y=12$