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The following table contains the rate of commission, number of items sold, and cost of each item for four different salespeople.

\begin{tabular}{|c|c|c|c|}
\hline
Salesperson & \begin{tabular}{l}
Rate of \\ commission
\end{tabular} & \begin{tabular}{l}
Number of \\ items sold
\end{tabular} & \begin{tabular}{l}
Cost of \\ each item
\end{tabular} \\
\hline
Arturo & [tex]$6.25\%$[/tex] & 8 & [tex]$\$[/tex]70[tex]$ \\
\hline
Dean & $[/tex]5.50\%[tex]$ & 14 & $[/tex]\[tex]$30$[/tex] \\
\hline
Ruth & [tex]$6.50\%$[/tex] & 7 & [tex]$\$[/tex]80[tex]$ \\
\hline
Salena & $[/tex]6.75\%[tex]$ & 15 & $[/tex]\[tex]$20$[/tex] \\
\hline
\end{tabular}

Assuming that each salesperson earned commission on all items he or she sold, who earned the most in commission?



Answer :

GinnyAnswer
First, let's determine the total commission earned by each salesperson based on their rate of commission, number of items sold, and the cost of each item.

1. Arturo:
- Rate of Commission: [tex]\(6.25\%\)[/tex]
- Number of Items Sold: 8
- Cost of Each Item: \[tex]$70 - To calculate the total commission, we use the formula: \[ \text{Total Commission} = \left(\frac{\text{Rate of Commission}}{100}\right) \times \text{Number of Items Sold} \times \text{Cost of Each Item} \] Substituting in the values: \[ \text{Total Commission} = \left(\frac{6.25}{100}\right) \times 8 \times 70 = 0.0625 \times 8 \times 70 = \$[/tex]35.00
\]

2. Dean:
- Rate of Commission: [tex]\(5.50\%\)[/tex]
- Number of Items Sold: 14
- Cost of Each Item: \[tex]$30 - Using the same formula: \[ \text{Total Commission} = \left(\frac{5.50}{100}\right) \times 14 \times 30 = 0.055 \times 14 \times 30 = \$[/tex]23.10
\]

3. Ruth:
- Rate of Commission: [tex]\(6.50\%\)[/tex]
- Number of Items Sold: 7
- Cost of Each Item: \[tex]$80 - Using the formula: \[ \text{Total Commission} = \left(\frac{6.50}{100}\right) \times 7 \times 80 = 0.065 \times 7 \times 80 = \$[/tex]36.40
\]

4. Salena:
- Rate of Commission: [tex]\(6.75\%\)[/tex]
- Number of Items Sold: 15
- Cost of Each Item: \[tex]$20 - Using the formula: \[ \text{Total Commission} = \left(\frac{6.75}{100}\right) \times 15 \times 20 = 0.0675 \times 15 \times 20 = \$[/tex]20.25
\]

Now we have the total commissions earned by each salesperson:
- Arturo: \[tex]$35.00 - Dean: \$[/tex]23.10
- Ruth: \[tex]$36.40 - Salena: \$[/tex]20.25

Comparing these amounts, we see that Ruth earned the highest commission, which was \$36.40.

Thus, Ruth earned the most in commission.

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