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

To write a system of equations, define 'x' as the total sales. Find the total sales needed to earn the same income from different pay scales. Determine the better offer by comparing the total income.

Step-by-step explanation:

To write a system of equations to represent the situation, let's define the total sales as 'x'.

The first scenario gives Kenisha a base salary of $500 plus a 4% commission. This can be represented as: y = 500 + 0.04x.

The second scenario gives Kenisha a base salary of $400 plus a 5% commission. This can be represented as: y = 400 + 0.05x.

To find the total price of the athletic shoes Kenisha needs to sell to earn the same income from each pay scale, set the two equations equal to each other and solve for x: 500 + 0.04x = 400 + 0.05x.

After solving the equation, we find that x = 2000. Therefore, Kenisha needs to sell a total of $2000 worth of athletic shoes to earn the same income from each pay scale.

To determine which offer is better, we need to compare the total income for each pay scale. Plug in the value of x into either of the equations to find the total income.

Answer 2

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.