# The larger of two numbers is 5 less than twice the smaller number. The sum of the two numbers is 28. How do you find the two numbers?

Nov 8, 2016

The numbers are $11 \mathmr{and} 17$

#### Explanation:

This question can be answered by using either 1 or 2 variables.
I will opt for 1 variable, because the second can be written in terms of the first. Define the numbers and variable first:

Let the smaller number be $x$.

The larger is "5 less than double $x$"

The larger number is $2 x - 5$

The sum of the numbers is 28. Add them to get $28$

$x + 2 x - 5 = 28 \text{ } \leftarrow$ now solve the equation for $x$

$3 x = 28 + 5$

$3 x = 33$

$x = 11$

The smaller number is $11$.
The larger is $2 \times 11 - 5 = 17$

$11 + 17 = 28$