# The square of Mark's age 3 years ago is 6 times the age he will be in 9 years. What is his age now?

Mar 16, 2018

15 years old

#### Explanation:

If we denote Mark's age today by $x$ we can set up an equation to solve.

We know that ${\left(x - 3\right)}^{2}$, "the square of his age three years ago", is 6 times greater than "his age in 9 years", $\left(x + 9\right)$, so to make this problem solvable we must create an expression where these two equal each other.

Thus by multiplying $\left(x + 9\right)$ by 6, we set "his age in 9" years to be equal to "the square of his age 3 years ago", creating the following expression:

${\left(x - 3\right)}^{2} = 6 \left(x + 9\right)$

Which, when simplified, leads us to a quadratic equation:

${x}^{2} - 12 x - 45 = 0$

$0 = \left(x - 15\right) \left(x + 3\right)$

Hence the two possible answers are:

${x}_{1} = 15$ and ${x}_{2} = - 3$

Obviously, you cannot be -3 years old, so he must be 15 years old.