To solve this problem, we calculate Sean's total sales based on the given graduated commission structure.

Commission Breakdown:

1. First $10,000 of sales: 1.75%
2. Next $27,000 of sales: 4.00%
3. Sales exceeding $37,000: 7.25%

Sean's total commission is $3,212.50. We will determine his sales by working backward through the commission structure.

Step 1: Maximum commission for first $37,000 of sales

• Commission on the first $10,000:
  $10,000 \times 0.0175 = 175 \, \text{dollars}$
• Commission on the next $27,000:
  $27,000 \times 0.04 = 1,080 \, \text{dollars}$

Total commission for $37,000 of sales = $175 + 1,080 = 1,255 \, \text{dollars}$.

Step 2: Remaining commission from sales above $37,000

Sean's total commission is $3,212.50. Subtract the $1,255 earned from the first $37,000: $3,212.50 - 1,255 = 1,957.50$

This additional $1,957.50 comes from sales above $37,000 at a 7.25% rate.

Step 3: Sales generating $1,957.50 at 7.25%

To find these sales, divide the additional commission by the rate: $\text{Sales above } 37,000 = \frac{1,957.50}{0.0725} \approx 27,000$

Step 4: Total sales

Sean's total sales are the sum of:

1. $37,000 from the first two commission brackets.
2. $27,000 from sales above $37,000.

$\text{Total sales} = 37,000 + 27,000 = 64,000$

Final Answer:

Sean's total sales for the month were $64,000.

Would you like a detailed explanation of any step?

Related Questions:

1. What would Sean's commission be if his sales were $50,000?
2. How much sales would Sean need to earn $4,000 in commission?
3. What percentage of Sean's total commission comes from sales above $37,000?
4. How does increasing the first commission rate to 2% affect his total commission?
5. What if Sean's sales were below $37,000—how would his commission be calculated?

Tip:

Always break down tiered commission problems step-by-step, starting from the base level.