Question

Liz earns a salary of $2,100 per month, plus a commission of 5% of her sales. She wants to earn at least $2,400 this month. How do you write an inequality to find amounts of sales that will meet her goal?

Answer 1

Hello! She earns a salary of $2,100, which is the fixed amount each month, plus 5% commission on her sales. To find out the amount of sales that will help her reach her goal, set up the inequality like this:

2,100 + 0.05x ≥ 2,400

We set it up like this, because $2,100 is the one-time price per month, and she earns 5% of her sales as commission. Plus, the key words "at least" means the inequality sign is greater than or equal to (≥)

How to solve this:

First off, subtract 2,100 from both sides, when you do, you get 0.05x ≥ 300. Now, divide each side by 0.05 to isolate the "x". 300/0.05 is 6,000. Let's check this. 6,000 * 5% (0.05) is 300. There. x = 6,000. Liz will need to sell $6,000 worth of items this month in order to meet her goal.