Question

Question #be0a3

Answer 1

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 `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`