Question

Dan earns a commission on the sells he makes each month

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

Enter only a number in the box.

Answer 1

Let \( x \) be the total sales Dan made last month.

1. If \( x \leq 20000 \):
\[
\text{Commission} = 0.05x
\]
Setting this equal to \( 1900 \):
\[
0.05x = 1900 \\
x = \frac{1900}{0.05} = 38000
\]
But this is not possible because \( x \) cannot exceed 20000 if he were earning only 5% commission.

2. If \( x > 20000 \):
The commission structure is:
\[
\text{Commission from first } 20000 = 0.05 \cdot 20000 = 1000
\]
The remaining sales would be \( x - 20000 \), for which Dan earns 3% commission:
\[
\text{Commission on remaining } (x - 20000) = 0.03(x - 20000)
\]
Thus, the total commission is:
\[
1000 + 0.03(x - 20000) = 1900
\]

Now we can solve for \( x \):
\[
1000 + 0.03(x - 20000) = 1900 \\
0.03(x - 20000) = 1900 - 1000 \\
0.03(x - 20000) = 900 \\
x - 20000 = \frac{900}{0.03} \\
x - 20000 = 30000 \\
x = 30000 + 20000 \\
x = 50000
\]

Thus, Dan's total sales last month were \(\boxed{50000}\).