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

Answer:

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.