# The product of two integers is 150. One integer is 5 less than twice the other. How do you find the integers?

##### 1 Answer
Jul 27, 2016

The integers are $\textcolor{g r e e n}{10}$ and $\textcolor{g r e e n}{15}$

#### Explanation:

Let the integers be $a$ and $b$
We are told:
$\textcolor{w h i t e}{\text{XXX}} a \cdot b = 150$
$\textcolor{w h i t e}{\text{XXX}} a = 2 b - 5$

Therefore
$\textcolor{w h i t e}{\text{XXX}} \left(2 b - 5\right) \cdot b = 150$

After simplifying
$\textcolor{w h i t e}{\text{XXX}} 2 {b}^{2} - 5 b - 150 = 0$

Factoring
$\textcolor{w h i t e}{\text{XXX}} \left(2 b + 15\right) \cdot \left(b - 10\right) = 0$

$\left.\begin{matrix}2 b + 15 = 0 & \text{ or " & b-10=0 \\ rarrb=15/2 & \null & rarr b=10 \\ "impossible" & \null & \null \\ "since b integer} & \null & \null\end{matrix}\right.$

So $b = 10$ and since $a = 2 b - 5 \rightarrow a = 15$