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.

Question

How much were her sales last week?

Answer 1

To find out how much Melissa sold last week, let's denote her total sales for the week as \( S \).

Step 1: Break down the sales and commissions.

• She earns 2% on the first $750 of sales.
• She earns 3% on any amount over $750.

Step 2: Calculate the commission for the first $750. For the first $750 of sales: \[ \text{Commission on first $750} = 0.02 \times 750 = 15. \]

Step 3: Determine the commission on the amount exceeding $750. If \( S \) is greater than $750, the amount over $750 is: \[ S - 750. \] The commission on this amount at a 3% rate is: \[ \text{Commission on amount over $750} = 0.03 \times (S - 750). \]

Step 4: Set up the total commission equation. The total commission earned by Melissa can be expressed as: \[ \text{Total Commission} = \text{Commission on first $750} + \text{Commission on amount over $750}. \] Given she earned $37.50, we can write: \[ 15 + 0.03 \times (S - 750) = 37.50. \]

Step 5: Solve for \( S \). First, isolate the commission on the amount over $750: \[ 0.03 \times (S - 750) = 37.50 - 15. \] Calculating the right side: \[ 37.50 - 15 = 22.50. \] So, we have: \[ 0.03 \times (S - 750) = 22.50. \] Now, divide both sides by 0.03: \[ S - 750 = \frac{22.50}{0.03}. \] Calculating the division: \[ \frac{22.50}{0.03} = 750. \] Now add 750 to both sides: \[ S = 750 + 750 = 1500. \]

Conclusion: Thus, Melissa's total sales last week were \(\boxed{1500}\).