# Stephanie s age is 4 years less than 3 times Matthew's age. If the product of their ages is 260, how old is Stephanie?

Dec 7, 2016

Stephanie is 26.

#### Explanation:

First, let's call Stephanie's age $s$ and Matthews age $m$:

Now, we can write the two sentences in terms of a math equation:

$s = 3 m - 4$

$s \cdot m = 260$

Now, because the first equation is already in terms of $s$ we can substitute $3 m - 4$ into the second equation for $s$ and solve for $m$:

$\left(3 m - 4\right) m = 260$

$3 {m}^{2} - 4 m = 260$

$3 {m}^{2} - 4 m - 260 = 260 - 260$

$3 {m}^{2} - 4 m - 260 = 0$

$\left(3 m + 26\right) \left(m - 10\right) = 0$

Now we can solve each term for $0$:

$3 m + 26 = 0$

$3 m + 26 - 26 = 0 - 26$

$3 m = - 26$

$\frac{3 m}{3} = - \frac{26}{3}$

$m = - \frac{26}{3}$

and

$m - 10 = 0$

$m - 10 + 10 = 0 + 10$

$m = 10$

Because age cannot be negative we will use $10$ to substitute for $m$ in the first equation and calculate $s$:

$s = 3 \cdot 10 - 4$

$s = 30 - 4$

$s = 26$