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?

1 Answer
Jan 8, 2017

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/100x100.

The expression for Plan A can be written as:

450 + 8/100s450+8100s where ss is the sales for the month.

The expression for Plan B can be written as:

695 + 3/100s695+3100s

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 + 3/100s450+8100s>695+3100s

450 + 8/100s - color(red)(450) - color(blue)(3/100s) > 695 + 3/100s - color(red)(450) - color(blue)(3/100s) 450+8100s4503100s>695+3100s4503100s

450 - color(red)(450) + 8/100s - color(blue)(3/100s) > 695 - color(red)(450) + 3/100s - color(blue)(3/100s)450450+8100s3100s>695450+3100s3100s

0 + 8/100s - color(blue)(3/100s) > 695 - color(red)(450) + 00+8100s3100s>695450+0

8/100s - color(blue)(3/100s) > 695 - color(red)(450)8100s3100s>695450

(8/100 - color(blue)(3/100))s > 245(81003100)s>245

5/100s > 2455100s>245

color(red)(100)/color(blue)(5) xx 5/100s > color(red)(100)/color(blue)(5) xx 2451005×5100s>1005×245

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.