# The sum of two numbers is -16. Three times the larger equals the smaller. How do you find the larger number?

Jan 5, 2017

The larger number is $- 4$.

#### Explanation:

Consider the numbers to be $x$ and $y$ with $x$ as the larger number. From the data, we can write:

$x + y = - 16$
$3 x = y$

From the second equation, we have a value for $y$.

In the first equation, substitute $y$ with $\textcolor{red}{3 x}$.

$x + y = - 16$

$x + \textcolor{red}{3} x = - 16$

$4 x = - 16$

Divide both sides by $4$.

$x = - 4$

In the second equation, substitute $x$ with $\textcolor{b l u e}{- 4}$.

$3 x = y$

$3 \left(\textcolor{b l u e}{-} 4\right) = y$

$- 12 = y$ or $y = - 12$