Question

The larger of two numbers is 1 less than 8 times the smaller. Their sum is 179. How do you find the numbers?

Answer 1

The two numbers are `20` and `159`

Explanation:

Define
`color(white)("XXX")b =`bigger (larger) number
`color(white)("XXX")s =`smaller number

We are told
[1]`color(white)("XXX")b = 8s-1`
[2]`color(white)("XXX")b+s=179`

Substituting `(8s-1)` for `b` (from [1]) into [2]
[3]`color(white)("XXX")8s-1+s = 179`

Simplify
[4]`color(white)("XXX")9s=180`

[5]`color(white)("XXX")s=20`

Substituting `20` for `s` in [2]
[6]`color(white)("XXX")b+20=179`

[7]`color(white)("XXX")b=159`