# The second of two numbers is 5 more than twice the first. The sum of the numbers is 44. How do you find the numbers?

Sep 25, 2015

$x = 13$
$y = 31$

#### Explanation:

You have two unknown numbers, we shall name them $x$ and $y$.

Then we look at the information about these unknowns that is given, and write them out to get a picture of the situation.

The second number, which we have called $y$, is 5 more than twice the first. To represent this, we write
$y = 2 x + 5$
where $2 x$ comes from 'twice the first', and
$+ 5$ comes from '5 more'.

The next piece of information states that the sum of $x$ and $y$ is 44. We represent this as $x + y = 44$.

Now we have two equations to work off.

To find $x$, substitute $y = 2 x + 5$ into $x + y = 44$.
We then get
$x + \left(2 x + 5\right) = 44$
$3 x + 5 = 44$
$3 x = 44 - 5$
$3 x = 39$
$x = \frac{39}{3}$
$x = 13$

Now we know the value of $x$, we can use it to find $y$.
We take the 2nd equation, and plug in $x = 13$.
$x + y = 44$
$13 + y = 44$
$y = 44 - 13$
$y = 31$