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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}{|l|l|l|l|}
\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?

A. Salena
B. Arturo
C. Ruth
D. Dean



Answer :

GinnyAnswer
Let's determine who earned the most commission by following these steps for each salesperson:

1. Calculate the total sales for each individual:
- Multiply the number of items sold by the cost of each item.

2. Calculate the commission:
- Multiply the total sales by the rate of commission (expressed as a decimal).

3. Compare the commissions to find who earned the most.

Let's go through the calculations for each salesperson:

### Arturo:
- Rate of commission: 6.25%
- Number of items sold: 8
- Cost of each item: \[tex]$70 \[ \text{Total sales for Arturo} = 8 \times 70 = \$[/tex]560
\]
[tex]\[ \text{Commission earned by Arturo} = 560 \times \frac{6.25}{100} = 560 \times 0.0625 = \$35.00 \][/tex]

### Dean:
- Rate of commission: 5.50%
- Number of items sold: 14
- Cost of each item: \[tex]$30 \[ \text{Total sales for Dean} = 14 \times 30 = \$[/tex]420
\]
[tex]\[ \text{Commission earned by Dean} = 420 \times \frac{5.50}{100} = 420 \times 0.055 = \$23.10 \][/tex]

### Ruth:
- Rate of commission: 6.50%
- Number of items sold: 7
- Cost of each item: \[tex]$80 \[ \text{Total sales for Ruth} = 7 \times 80 = \$[/tex]560
\]
[tex]\[ \text{Commission earned by Ruth} = 560 \times \frac{6.50}{100} = 560 \times 0.065 = \$36.40 \][/tex]

### Salena:
- Rate of commission: 6.75%
- Number of items sold: 15
- Cost of each item: \[tex]$20 \[ \text{Total sales for Salena} = 15 \times 20 = \$[/tex]300
\]
[tex]\[ \text{Commission earned by Salena} = 300 \times \frac{6.75}{100} = 300 \times 0.0675 = \$20.25 \][/tex]

### Comparing Commissions:

- Arturo: \[tex]$35.00 - Dean: \$[/tex]23.10
- Ruth: \[tex]$36.40 - Salena: \$[/tex]20.25

The highest commission was earned by Ruth with \$36.40. Therefore, the salesperson who earned the most in commission is:

C. Ruth

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