Modeling with Linear Functions

Question

When hired at a new job selling jewelry, you are given two pay options:

Option A: Base salary of $13,000 a year, with a commission of 9% of your sales

Option B: Base salary of $18,000 a year, with a commission of 5% of your sales

In order for option A to produce a larger income, you would need to sell how much jewelry each year?

Answer 1

We can model this using a set of equations.

y = 13,000 + .09x (salary option A)

y = 18,000 + .05x (salary option B)

Where y is the amount of money you will make in a year, and x is the amount of sales you make in the same year.

In order to find how many sales are needed for option A to be optimal, we should find where the salary options are equal. We can find that by finding the intersection of the two equations.

If we set them equal to each other:

13,000 + .09x = 18,000 + .05x

Subtract 13,000 from both sides

.09 x = 5,000 + .05x

Subtract .05x from each side

.04x = 5,000

Divide by .04

x = 125,000

If you make $125,000 in sales in a year, the two salary options are equal. Therefore, you need to make greater than $125,000 in sales of jewelry a year in order for option A to be optimal.

Answer 2