# The second of two numbers is 5 more than twice the first their sum is 80, what are the numbers?

Nov 16, 2016

The numbers are $25 \mathmr{and} 55$

#### Explanation:

Although there are two numbers, we can define both of them using one variable.

Let the first, smaller number be $x$.

This is doubled, so $2 x$, then 5 is added to get the second number.

The second number is $2 x + 5$

"The sum of the numbers is $80$"

$x + 2 x + 5 = 80 \text{ } \leftarrow$ solve the equation to find x.

$3 x = 80 - 5$

$3 x = 75$

$x = \frac{75}{3}$

$x = 25$

One number is $25$, the other is $2 \times 25 + 5 = 55$

$25 + 55 = 80$