Question

Kenisha sells athletic shoes part-time at the department store. She can earn either $500 plus a 4% commission on her total sales, or $400 plus a 5% commission on total sales.
a. Write a system of equations to represent the situation.

b. What is the total price of the athletic shoes Kenisha needs to sell to earn the same income from each pay scale?

c. Which is the better offer?

Answer 1

Plan 'A' total compensation = x
plan 'B' total compensation = y 
let z = total sales 
x = 500 + 0.04z
y = 400 + 0.05z 
the better offer DEPENDS on the total sales that Kenisha makes 
the point at which the two plans are the same is found by making the x and y equal: 
500 + 0.04z = 400 + 0.05z 
100 = 0.01z 
z = 10,000 
so 
if Kenisha sells EXACTLY $10,000 per month both plans give her the same compensation so no plan is "better" 
if Kenisha sells LESS than $10,000 per month, then plan 'A' is "better" for her in terms of compensation. That is because the $100 that she gains on the base salary from plan 'A' is bigger than the 1% sales commission she loses on total sales (which is less than $10,000) 
if Kenisha sells MORE than $10,000 per month, then plan 'B' is "better" for her in terms of compensation. That is because the extra 1% sales commission she makes on total sales (which is more than $10,000) is more than the $100 loss she takes on the base salary amount.