Let's analyze the sales and earnings for each employee based on their commission structure for the month of February:
1. Employee \#1:
- Earnings: 4.7 thousand dollars.
- Commission structure: [tex]$2,000 + 3\%$[/tex] of all sales.
To find the sales, we set up the equation:
[tex]\[
2000 + 0.03 \times \text{sales} = 4700
\][/tex]
Solving for sales:
[tex]\[
0.03 \times \text{sales} = 4700 - 2000
\][/tex]
[tex]\[
0.03 \times \text{sales} = 2700
\][/tex]
[tex]\[
\text{sales} = \frac{2700}{0.03} = 90000 \text{ dollars}
\][/tex]
2. Employee \#2:
- Earnings: 4.9 thousand dollars.
- Commission structure: [tex]$7\%$[/tex] of all sales.
To find the sales, we set up the equation:
[tex]\[
0.07 \times \text{sales} = 4900
\][/tex]
Solving for sales:
[tex]\[
\text{sales} = \frac{4900}{0.07} = 70000 \text{ dollars}
\][/tex]
3. Employee \#3:
- Earnings: 4.4 thousand dollars.
- Commission structure: [tex]$5\%$[/tex] on the first \[tex]$40,000 and $[/tex]8\%[tex]$ on anything over \$[/tex]40,000.
To find the sales, we need to consider the two different commission rates.
Let's determine whether the earnings are only from the [tex]$5\%$[/tex] commission on the first \[tex]$40,000.
\[
0.05 \times 40000 = 2000 \text{ dollars}
\]
Since earnings exceed 2000 dollars, there must be additional sales earning the $[/tex]8\%[tex]$ commission:
\[
0.05 \times 40000 + 0.08 \times (\text{sales} - 40000) = 4400
\]
Solving this equation:
\[
2000 + 0.08 \times (\text{sales} - 40000) = 4400
\]
\[
0.08 \times (\text{sales} - 40000) = 2400
\]
\[
\text{sales} - 40000 = \frac{2400}{0.08} = 30000
\]
\[
\text{sales} = 40000 + 30000 = 70000 \text{ dollars}
\]
Thus, the sales for each employee are as follows:
- Employee \#1: \$[/tex]90,000
- Employee \#2: \[tex]$70,000
- Employee \#3: \$[/tex]70,000
Employee \#1 did not have the same dollar amount in sales as Employee \#2 and Employee \#3.
Therefore, the answer is:
a. Employee \#1.
