# The sum of two numbers if 67. the smaller number is 3 less than the larger number. what are the 2 numbers?

Jan 19, 2018

Set up a system of equations.

#### Explanation:

I am going to use x for the smaller number and y for the larger one.

The sum of both these numbers is 67, so the equation should be:
$x + y = 67$

Since the smaller number is three less than the larger number, that means 3 has to be added to the smaller number to make it equal in size to the larger number.
$x + 3 = y$

To solve the equation, simply plug in $x + 3$ for the y variable in the first equation.

$x + x + 3 = 67 \rightarrow$ Rewrite the first equation

$2 x = 64 \rightarrow$ Subtract 3 from each side, combine like terms

$x = 32 \rightarrow$ Divide each side by 2

The smaller number is 32, so we plug that in to the second equation to find the larger number.

$32 + 3 = y$

$y = 35$

The two numbers are 32 and 35

Jan 19, 2018

$35$ and $32$

#### Explanation:

Let's say $x < y$

$x + y = 67$

$x = y - 3$

$\therefore$

$y - 3 + x 67$

$2 x - 3 = 67$

$2 y = 70$

$y = 35$

Now we solve for $x$

$x + 35 = 67$

$x = 32$