Question

Melissa earns a 2% commission on the first $750 of sales she makes each week. She earns a 3% commission on the amount of her sales that are greater than $750 each week. Melissa earned $37.50 in commissions last week.

How much were her sales last week?
Enter your answer as a number, like this: 42
(not multiple choice)

Answer 1

Let's assume that Melissa's total sales last week were x dollars. Then, we can set up the following equation to represent her commission:

0.02 * min(x, 750) + 0.03 * max(x - 750, 0) = 37.5

Here, the first term represents the commission on the first $750 of sales, and the second term represents the commission on any sales above $750. The max function ensures that the second term is only calculated for sales above $750, while the min function ensures that the first term is only calculated for the first $750 of sales.

We can solve this equation for x:

0.02 * min(x, 750) + 0.03 * max(x - 750, 0) = 37.5
0.02 * 750 + 0.03 * max(x - 750, 0) = 37.5
15 + 0.03 * max(x - 750, 0) = 37.5
0.03 * max(x - 750, 0) = 22.5
max(x - 750, 0) = 750

Since the maximum function is equal to 750, we know that x - 750 = 750, which implies that x = 1500.

Therefore, Melissa's total sales last week were $1500.