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?

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 \(\boxed{1500}\).