Question

Dan earns 5% in commission on total sales up to 20,000.
he earns a 3% commission on any amount over 20,000
if he earned 35,000 in sales what amount of commission in dollars he earn
dan earned 1,900 in commission last month how much money he earned

Answer 1

To calculate Dan's commission based on his sales of $35,000, we can break it down as follows:

1. **Calculate the commission on the first $20,000**:
- **Commission Rate**: 5%
- **Sales Amount**: $20,000
- **Commission** = \( 20,000 \times 0.05 = 1,000 \) dollars

2. **Calculate the commission on the amount over $20,000**:
- **Sales Amount over $20,000**: \( 35,000 - 20,000 = 15,000 \)
- **Commission Rate**: 3%
- **Commission** = \( 15,000 \times 0.03 = 450 \) dollars

3. **Total Commission**:
- **Total Commission** = \( 1,000 + 450 = 1,450 \) dollars

### Summary of Commission Calculation
- Total Sales: $35,000
- Total Commission Earned: **$1,450**

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Now, regarding the second part of your question:

If Dan earned $1,900 in commission last month, we can calculate the sales amount based on the commission structure:

1. **Let \( x \) be the total sales amount.**
- If his sales are up to $20,000, his commission is \( 0.05x \).
- If sales exceed $20,000, we need to break it into two parts:

1. **If \( x \leq 20,000 \)**:
- \( 0.05x = 1,900 \)
- \( x = \frac{1,900}{0.05} = 38,000 \) (impossible, since sales can't exceed $20,000 for this part)

2. **If \( x > 20,000 \)**:
- Let \( y = x - 20,000 \) (the amount over $20,000)
- Thus, the commission can be expressed as:
\[
1,000 + 0.03y = 1,900
\]
\[
0.03y = 1,900 - 1,000 = 900
\]
\[
y = \frac{900}{0.03} = 30,000
\]

3. **Total Sales \( x \)**:
- \( x = y + 20,000 = 30,000 + 20,000 = 50,000 \)

### Summary of Commission Calculation for Last Month
- Total Commission Earned: $1,900
- Total Sales Amount: **$50,000**

In summary:
- His commission on $35,000 sales is **$1,450**.
- If his commission was $1,900 last month, he earned from **$50,000** in sales.