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+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 :

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.