(a)

Question

A salesperson earns commission on the sales that she makes each month.

• The salesperson earns a 5%
commission on the first 5000
she has in sales.
• The salesperson earns a 7.5%
commission on the amount of her sales that are greater than 5000.


Part B
​The salesperson earned
$
1
,
375
$1,375 in commission last month. How much money, in dollars, did she have in sales last month?
​Enter your answer in the box.
​

Answer 1

To solve for the total sales of the salesperson, we can set up an equation based on the commission structure provided.

1. Commission Structure:

   • For the first $5,000 in sales, the commission is 5%.
   • For sales over $5,000, the commission is 7.5%.

2. Commission Calculation:

   • If the total sales \( S \) is less than or equal to $5,000: \[ \text{Commission} = 0.05 \cdot S \]

   • If \( S \) is greater than $5,000: \[ \text{Commission} = (0.05 \cdot 5000) + (0.075 \cdot (S - 5000)) \]

   The commission on the first $5,000: \[ 0.05 \cdot 5000 = 250 \]

   Thus, for \( S > 5,000 \): \[ \text{Commission} = 250 + 0.075 \cdot (S - 5000) \]

3. Set Up the Equation: We know the commission earned is $1,375: \[ 250 + 0.075 \cdot (S - 5000) = 1375 \]

4. Solve for \( S \):

   • Subtract 250 from both sides: \[ 0.075 \cdot (S - 5000) = 1375 - 250 \] \[ 0.075 \cdot (S - 5000) = 1125 \]

   • Divide by 0.075: \[ S - 5000 = \frac{1125}{0.075} \] \[ S - 5000 = 15000 \]

   • Add 5000 to both sides: \[ S = 15000 + 5000 \] \[ S = 20000 \]

Therefore, the total sales last month were $20,000.