# The sum of two number is 118 and their difference is 16.find the numbers?

May 16, 2018

$51$ and $67$

#### Explanation:

$x + y = 118$
$x - y = 16$

solve for $x$ in terms of $y$

$x - y + y = 16 + y$

$x = 16 + y$

Put $16 + y$ in the first equation in place of $x$

$16 + y + y = 118$ Combine $y$'s

$2 y + 16 = 118$ Subtract $16$ from both sides

$2 y + 16 - 16 = 118 - 16$ this gives

$2 y = 102$ divide both sides by $2$

$2 \frac{y}{2} = \frac{102}{2}$ so

$y = 51$

$x = 16 + y$

$x = 16 + 51$

$x = 67$