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.
