# If two numbers are in the ratio 5 to 3 and the sum of the numbers is -24, what is the smaller number?

Oct 25, 2016

The number the furthest to the left on the number line is $- 15$.

#### Explanation:

Let the numbers be $x$ and $y$.

$5 x = 3 y$
$x + y = - 24$

Solve using substitution.

$y = - 24 - x$

$5 x = 3 \left(- 24 - x\right)$

$5 x = - 72 - 3 x$

$8 x = - 72$

$x = - 9$

$\therefore - 9 + y = - 24$

$y = - 15$