Let's determine the total earnings [tex]\( E \)[/tex] for Sam based on his hourly wages and the tips he earns per person served.
1. Hourly Wages:
- Sam earns [tex]$\$[/tex]5[tex]$ per hour.
- Sam works for 6 hours.
- Therefore, the total wages Sam earns just from working is calculated as:
\[
\text{total wages} = 5 \, \text{dollars/hour} \times 6 \, \text{hours} = 30 \, \text{dollars}
\]
2. Tips:
- Sam earns $[/tex]\[tex]$3$[/tex] in tips for each person he serves.
- Let [tex]\( n \)[/tex] be the number of people Sam serves in that day.
- Therefore, the total tips Sam earns is:
[tex]\[
\text{total tips} = 3 \, \text{dollars/person} \times n \, \text{people} = 3n \, \text{dollars}
\][/tex]
3. Total Earnings:
- To find Sam’s total earnings [tex]\( E \)[/tex] for the day, we need to add his total wages and his total tips:
[tex]\[
E = \text{total wages} + \text{total tips}
\][/tex]
Substituting the values we have:
[tex]\[
E = 30 + 3n
\][/tex]
Thus, the function Sam can use to figure out his total earnings [tex]\( E \)[/tex] for the day, considering he serves [tex]\( n \)[/tex] people, is:
[tex]\[
E(n) = 3n + 30
\][/tex]
So, the correct option is:
C. [tex]\( E(n) = 3n + 30 \)[/tex]
