Question

Dauzat Pretest 2017 grade 7 RP

He earns a 5% commision on total sales up to $20000
He earns a 3% commision on any amount over $20000
Dan earned $1,900 in commission last month. How much money, in dollars, did he have in sales last month?

Answer 1

To find out how much money Dan had in sales last month, we can break this down based on the commission structure he has.

1. **Commission Calculation**:
- For sales up to $20,000, he earns 5% commission.
- For sales exceeding $20,000, he earns 3% on the amount over $20,000.

2. **Setting Up the Equation**:
Let's denote the total sales amount as \( S \).

If \( S \) is less than or equal to $20,000:
\[
\text{Commission} = 0.05S
\]

If \( S \) is greater than $20,000:
\[
\text{Commission} = 0.05(20000) + 0.03(S - 20000)
\]
Simplifying:
\[
\text{Commission} = 1000 + 0.03(S - 20000)
\]
\[
\text{Commission} = 1000 + 0.03S - 600
\]
\[
\text{Commission} = 0.03S + 400
\]

3. **Given Commission**:
Dan earned $1,900 in commission last month.

Now, we can set up two scenarios based on \( S \):

**Case 1**: \( S \leq 20,000 \)

\[
0.05S = 1900
\]
\[
S = \frac{1900}{0.05} = 38000 \quad (\text{Not possible, since } S \leq 20,000)
\]

**Case 2**: \( S > 20,000 \)

\[
0.03S + 400 = 1900
\]
\[
0.03S = 1900 - 400
\]
\[
0.03S = 1500
\]
\[
S = \frac{1500}{0.03} = 50000
\]

Thus, the total sales amount that Dan had last month is **$50,000**.