How do you translate the following into a equation and solve: "The sum of two numbers is eighteen. Two less than three times the smaller is equal to the larger."?

Mar 9, 2017

The smaller number $x = 5$, and the larger number $y = 13$

Explanation:

"The sum of two numbers is eighteen. Two less than three times the smaller is equal to the larger."

Let $x$ be the smaller number, and let $y$ be the larger number.

$x + y = 18$

$- 2 + 3 x = y$
$\implies \textcolor{b l u e}{y = 3 x - 2}$

Use substitution to find the values of the two numbers.
$x + \textcolor{b l u e}{\left(3 x - 2\right)} = 18$
$4 x - 2 = 18$
$4 x = 20$
$\textcolor{red}{x = 5}$

$y = 3 \textcolor{red}{\left(5\right)} - 2$
$y = 13$