To determine which employee did not have the same dollar amount in sales for the month of February as the other two employees, we need to calculate the sales for each employee using their respective earnings formulae and compare the results. Here's a step-by-step breakdown:
1. Employee #1:
- Earnings in February: \[tex]$4.7 thousand or \$[/tex]4,700
- Formula: [tex]\(\text{Earnings} = \$2,000 + 3\% \text{ commission on all sales}\)[/tex]
- Rearrange the formula to solve for sales:
[tex]\[
\text{Earnings} = 2000 + 0.03 \times \text{Sales}
\][/tex]
Solving for Sales:
[tex]\[
\text{Sales} = \frac{\text{Earnings} - 2000}{0.03} = \frac{4700 - 2000}{0.03} = \frac{2700}{0.03} = 90000
\][/tex]
- Sales for Employee #1: \[tex]$90,000
2. Employee #2:
- Earnings in February: \$[/tex]4.9 thousand or \[tex]$4,900
- Formula: \(\text{Earnings} = 7\% \text{ commission on all sales}\)
- Rearrange the formula to solve for sales:
\[
\text{Earnings} = 0.07 \times \text{Sales}
\]
Solving for Sales:
\[
\text{Sales} = \frac{\text{Earnings}}{0.07} = \frac{4900}{0.07} = 70000
\]
- Sales for Employee #2: \$[/tex]70,000
3. Employee #3:
- Earnings in February: \[tex]$4.4 thousand or \$[/tex]4,400
- Formula: [tex]\(\text{Earnings} = 5\% \text{ commission on the first \$40,000} + 8\% \text{ commission on anything over \$40,000}\)[/tex]
- First, check if the earnings include amount over \[tex]$40,000 in sales:
\[
\text{Initial commission (up to \$[/tex]40,000 sales)} = 0.05 \times 40000 = 2000
\]
- Total earnings minus initial commission:
[tex]\[
\text{Earnings} - 2000 = 4400 - 2000 = 2400
\][/tex]
Remaining earnings from sales over \[tex]$40,000:
\[
\text{Remaining sales} = \frac{2400}{0.08} = 30000
\]
Total sales:
\[
\text{Total sales} = 40000 + 30000 = 70000
\]
- Sales for Employee #3: \$[/tex]70,000
Comparing the sales figures:
- Sales for Employee #1: \[tex]$90,000
- Sales for Employee #2: \$[/tex]70,000
- Sales for Employee #3: \$70,000
Employee #1 has different sales than Employee #2 and Employee #3.
Answer:
a. Employee #1
