Question

Dan earned $1,900 in commission last month. How much money, in dollars, did he have in sales last month?


he earns a 5% commission on total sales up to 20,000

he earns a 3 % commission on any amount over 20,000

Answer 1

To find out how much Dan had in sales last month, we need to break it down based on the commission structure provided.

1. **Calculate the sales for the first $20,000:**
Dan earns a 5% commission on sales up to $20,000. Therefore, if his total sales were $20,000 or less, we can calculate his commission from this amount as follows:

\[
\text{Commission from } \$20,000 = 0.05 \times 20,000 = 1,000
\]

Since Dan earned $1,900 in commission, he must have generated sales over $20,000 because $1,000 is less than $1,900.

2. **Calculate the commission from sales over $20,000:**
Let \( S \) be the total sales amount. If \( S \) exceeds $20,000, then the commission can be expressed as:

\[
\text{Commission} = 0.05 \times 20,000 + 0.03 \times (S - 20,000)
\]

Substituting the maximum commission earned for the first $20,000:

\[
1,000 + 0.03 \times (S - 20,000) = 1,900
\]

3. **Set up the equation:**

\[
0.03 \times (S - 20,000) = 1,900 - 1,000
\]
\[
0.03 \times (S - 20,000) = 900
\]

4. **Solve for S:**

Dividing both sides by 0.03:

\[
S - 20,000 = \frac{900}{0.03}
\]
\[
S - 20,000 = 30,000
\]

Adding $20,000 to both sides gives us:

\[
S = 50,000
\]

Thus, Dan had **$50,000** in sales last month.