To determine which employee did not have the same dollar amount in sales for the month of February, we need to calculate the sales for each employee based on their earnings.
Given earnings for February:
- Employee #1: \[tex]$4.7 thousand
- Employee #2: \$[/tex]4.9 thousand
- Employee #3: \[tex]$4.4 thousand
1. Calculate sales for Employee #1:
- Earnings formula: \$[/tex]2000 + 3% of sales
- Earnings in dollars: \[tex]$4.7 thousand = \$[/tex]4700
- Let [tex]\( S_1 \)[/tex] be the sales for Employee #1
[tex]\[
4700 = 2000 + 0.03 \times S_1
\][/tex]
Solve for [tex]\( S_1 \)[/tex]:
[tex]\[
4700 - 2000 = 0.03 \times S_1
\][/tex]
[tex]\[
2700 = 0.03 \times S_1
\][/tex]
[tex]\[
S_1 = \frac{2700}{0.03} = 90000
\][/tex]
So, Employee #1's sales in dollars are \[tex]$90,000.
2. Calculate sales for Employee #2:
- Earnings formula: 7% of sales
- Earnings in dollars: \$[/tex]4.9 thousand = \[tex]$4900
- Let \( S_2 \) be the sales for Employee #2
\[
4900 = 0.07 \times S_2
\]
Solve for \( S_2 \):
\[
S_2 = \frac{4900}{0.07} = 70000
\]
So, Employee #2's sales in dollars are \$[/tex]70,000.
3. Calculate sales for Employee #3:
- Earnings formula: 5% of first \[tex]$40,000 + 8% of anything over \$[/tex]40,000
- Earnings in dollars: \[tex]$4.4 thousand = \$[/tex]4400
- Part of the earnings is 5% of \[tex]$40,000:
\[
0.05 \times 40000 = 2000
\]
- Remaining earnings come from 8% of sales over \$[/tex]40,000. Let [tex]\( S_3 \)[/tex] be the total sales for Employee #3 over \[tex]$40,000:
\[
4400 - 2000 = 0.08 \times (S_3 - 40000)
\]
\[
2400 = 0.08 \times (S_3 - 40000)
\]
Solve for \( S_3 \):
\[
2400 = 0.08 \times (S_3 - 40000)
\]
\[
S_3 - 40000 = \frac{2400}{0.08} = 30000
\]
\[
S_3 = 30000 + 40000 = 70000
\]
So, Employee #3's sales in dollars are \$[/tex]70,000.
To summarize the sales calculations:
- Employee #1: \[tex]$90,000
- Employee #2: \$[/tex]70,000
- Employee #3: \$70,000
Conclusion:
Employee #1 did not have the same dollar amount in sales as Employee #2 and Employee #3.
Thus, the correct answer is:
a. Employee #1.
