Answer :
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.
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.
