# The sum of two numbers is 80. lf three times the smaller number is subtracted from the larger number, the result is 16. How do you find the two numbers?

Dec 1, 2016

$x = 64$ and $y = 16$

#### Explanation:

First, let's call the two numbers we are looking for $x$ and $y$ and say $x$ is the larger number.

From the problem we know:

$x + y = 80$

We also know:

$x - 3 y = 16$

Solving the first equation for $x$ gives:

$x + y - y = 80 - y$

$x = 80 - y$

We can now substitute $80 - y$ for $x$ in the second equation and solve for $y$:

$80 - y - 3 y = 16$

$80 - 4 y = 16$

$80 - 80 - 4 y = 16 - 80$

$- 4 y = - 64$

$\frac{- 4 y}{-} 4 = \frac{- 64}{- 4}$

$y = 16$

Finally, we can substitute $16$ for $y$ in the solution to the first equation:

$x = 80 - 16$

$x = 64$