Question

Chris can be paid in one of two ways. Plan A is a salary of $450 per month, plus a commission of 8% of sales. Plan B is a salary of $695 per month, plus of 3% of sales. For what amount of sales is Chris better off selecting plan A?

Answer 1

See full explanation below.

Explanation:

First, when dealing with percents, "Percent" or "%" means "out of 100" or "per 100", Therefore x% can be written as `x/100`.

The expression for Plan A can be written as:

`450 + 8/100s` where `s` is the sales for the month.

The expression for Plan B can be written as:

`695 + 3/100s`

The question we are being asked is when is Plan A > Plan B. So, we can write and solve this inequality:

`450 + 8/100s > 695 + 3/100s`

`450 + 8/100s - color(red)(450) - color(blue)(3/100s) > 695 + 3/100s - color(red)(450) - color(blue)(3/100s)`

`450 - color(red)(450) + 8/100s - color(blue)(3/100s) > 695 - color(red)(450) + 3/100s - color(blue)(3/100s)`

`0 + 8/100s - color(blue)(3/100s) > 695 - color(red)(450) + 0`

`8/100s - color(blue)(3/100s) > 695 - color(red)(450)`

`(8/100 - color(blue)(3/100))s > 245`

`5/100s > 245`

`color(red)(100)/color(blue)(5) xx 5/100s > color(red)(100)/color(blue)(5) xx 245`

`cancel(color(red)(100))/cancel(color(blue)(5)) xx color(blue)(cancel(color(black)(5)))/color(red)(cancel(color(black)(100)))s > 24500/color(blue)(5)`

`s > 4900`

Plan A is better when sales for the month are greater than $4,900.