Answered

The table below shows the earnings, in thousands of dollars, for three different commissioned employees.

\begin{tabular}{|c|c|c|c|}
\hline & \begin{tabular}{c}
Employee \#1 \\
[tex]$\$[/tex] 2,000 + 3 \%[tex]$ on all \\
sales
\end{tabular} & \begin{tabular}{c}
Employee \#2 \\
$[/tex]7 \%[tex]$ on all sales
\end{tabular} & \begin{tabular}{c}
Employee \#3 \\
$[/tex]5 \%[tex]$ on the first $[/tex]\[tex]$ 40,000$[/tex] \\
[tex]$+ 8 \%$[/tex] on anything over \\
[tex]$\$[/tex] 40,000$
\end{tabular} \\
\hline December & 4.4 & 5.6 & 5.2 \\
\hline January & 3.5 & 3.85 & 3.6 \\
\hline February & 4.7 & 4.9 & 4.4 \\
\hline
\end{tabular}

Which employee did not have the same dollar amount in sales for the month of February as the other two employees?

A. Employee \#1
B. Employee \#2
C. Employee \#3
D. They each had the same dollar amount in sales.



Answer :

To solve this problem, let's calculate the sales amounts for each employee in February based on their earnings and commission structures.

### Employee \#1:
- Earnings: [tex]$4.7 \times 1000 = \$[/tex]4700[tex]$ - Commission Structure: \$[/tex]2000 base salary + 3% of sales

First, we calculate the part of the earnings that comes from the commission:
[tex]\[ \text{Commission earnings} = \$4700 - \$2000 = \$2700 \][/tex]

Next, we find the total sales [tex]\( S \)[/tex] using the 3% commission rate:
[tex]\[ 0.03 \times S = \$2700 \][/tex]
[tex]\[ S = \frac{\$2700}{0.03} \][/tex]
[tex]\[ S = \$90,000 \][/tex]

### Employee \#2:
- Earnings: [tex]$4.9 \times 1000 = \$[/tex]4900[tex]$ - Commission Structure: 7% of all sales We find the total sales \( S \) using the 7% commission rate: \[ 0.07 \times S = \$[/tex]4900 \]
[tex]\[ S = \frac{\$4900}{0.07} \][/tex]
[tex]\[ S = \$70,000 \][/tex]

### Employee \#3:
- Earnings: [tex]$4.4 \times 1000 = \$[/tex]4400[tex]$ - Commission Structure: 5% on the first \$[/tex]40,000 + 8% on anything over \[tex]$40,000 First, we calculate the earnings from the first \$[/tex]40,000:
[tex]\[ \text{Earnings from first \$40,000} = 0.05 \times \$40,000 = \$2000 \][/tex]

Next, we calculate the remaining earnings:
[tex]\[ \text{Remaining Earnings} = \$4400 - \$2000 = \$2400 \][/tex]

The remaining earnings come from sales over \[tex]$40,000: \[ 0.08 \times \text{Sales over \$[/tex]40,000} = \[tex]$2400 \] \[ \text{Sales over \$[/tex]40,000} = \frac{\[tex]$2400}{0.08} \] \[ \text{Sales over \$[/tex]40,000} = \[tex]$30,000 \] The total sales are: \[ S = \$[/tex]40,000 + \[tex]$30,000 = \$[/tex]70,000 \]

### Summary of Sales:

- Employee \#1: \[tex]$90,000 - Employee \#2: \$[/tex]70,000
- Employee \#3: \$70,000

Based on the calculations, Employee \#1 had a different sales amount compared to Employee \#2 and Employee \#3.

Thus, the employee who did not have the same dollar amount in sales for the month of February as the other two employees is:
a. Employee \#1.