# One number is three more than the other number. When the square of the smaller number is subtracted from the square of the smaller number, 45 is obtained. What are the two numbers?

Mar 23, 2017

Let the numbers be $x$ and $y$.

$\left\{\begin{matrix}x + 3 = y \\ \left(x + y\right) \left(y - x\right) = 45\end{matrix}\right.$

If we rearrange the first équation, we get $x - y = 3$. Substituting, we get:

$\left(x + \left(x + 3\right)\right) \left(3\right) = 45$

$2 x + 3 = 15$

$2 x = 12$

$x = 6$

$\therefore$The numbers are $6$ and $9$.

Hopefully this helps!

Mar 23, 2017

I got $6 \mathmr{and} 9$

#### Explanation:

let s call our numbers $x$ and $y$. We get:
$x = y + 3$
and
$\left(x + y\right) \left(x - y\right) = 45$
from the second we get:
${x}^{2} - {y}^{2} = 45$
substituting the first equation $x = y + 3$ we get:
${\left(y + 3\right)}^{2} - {y}^{2} = 45$
${y}^{2} + 6 y + 9 - {y}^{2} = 45$
$6 y = 36$
$y = \frac{36}{6} = 6$
so that $x = 6 + 3 = 9$

Mar 23, 2017

The first number is 9, and the second number is 6.

#### Explanation:

Let $n$ be the first number. The second number is therefore $n - 3$.

Sum of the numbers: $\textcolor{red}{\left(n\right) + \left(n - 3\right) = 2 n - 3}$
Difference of the numbers: $\textcolor{b l u e}{\left(n\right) - \left(n - 3\right) = 3}$

Equation:
$\textcolor{red}{\left(2 n - 3\right)} \textcolor{b l u e}{\left(3\right)} = 45$

$2 n - 3 = 15$

$2 n = 18$

$n = 9$ (First number)
$n - 3 = 6$ (Second number)