# How do you find two numbers whose sum is 49, if the greater number is 4 more than 8 times the smaller number?

Apr 5, 2017

I got $44 \mathmr{and} 5$

#### Explanation:

Call the numbers $x$ and $y$, you get:
$x + y = 49$
$x = 8 y + 4$
substitute the second equation into the first:
$8 y + 4 + y = 49$
$9 y = 45$
$y = \frac{45}{9} = 5$
so that:
$x = 8 \cdot 5 + 4 = 44$

Apr 5, 2017

Write two equations and solve for one variable. Then substitute the value for the first variable to find the value for the second variable.

#### Explanation:

The first equation would be
$x + y = 49$

Where x = the first variable
Where y = the second variable.

The second equation would be

$y = 8 x + 4$

where y = the larger number.

Put $8 x + 4$ into the first equation in place of y this gives.

$x + 8 x + 4 = 49$ solve the equation for x by combining terms

$9 x + 4 = 49$ subtract 4 from both sides

$9 x + 4 - 4 = 49 - 4$ this gives

$9 x = 45$ Divide both sides by 9 gives

$9 \frac{x}{9} = \frac{45}{9}$ The answer is

$x = 5$ Now put 5 into one of the equation to find y

$y = 8 \left(5\right) + 4$

$y = 44$

To check put the values into the first equation

$5 + 44 = 49$

x = 5 : y = 44