Question #be0a3

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Answer 1 · 2017-03-13T22:34:31

larger number $= 31$

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 $2L$ .

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

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

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

Simplify by adding like terms:
$2L +3L -8 = 147 -3L +3L$
$5L -8 = 147$
$5L -8 +8 = 147 + 8$
$5L = 155$
$L = 155/5 = 31$

$S = 49 - 31 = 18$