# Question #be0a3

Mar 13, 2017

larger number $= 31$

#### Explanation:

Create two equations using two variables:
$S$ = smaller number
$L$ = larger number

equation 1: $S + L = 49$ and rearrange: $S = 49 - L$

To make them equal subtract $8$ from $2 L$.

equation 2: $2 L - 8 = 3 S$

Substitute equation 1 into equation 2: $2 L - 8 = 3 \left(49 - L\right)$

Distribute the right side: $2 L - 8 = 147 - 3 L$

$2 L + 3 L - 8 = 147 - 3 L + 3 L$
$5 L - 8 = 147$
$5 L - 8 + 8 = 147 + 8$
$5 L = 155$
$L = \frac{155}{5} = 31$
$S = 49 - 31 = 18$