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Sam is a waiter at a local restaurant where he earns [tex]$5 per hour and about $[/tex]3 in tips for each person he serves. Sam works 6 hours on a particular day.

If [tex]\( n \)[/tex] represents the number of people Sam serves that day, which of the following functions could Sam use to figure [tex]\( E \)[/tex], his total earnings for the day?

A. [tex]\( E(n) = 5n + 18 \)[/tex]
B. [tex]\( E(n) = 3n \)[/tex]
C. [tex]\( E(n) = 3n + 30 \)[/tex]



Answer :

GinnyAnswer
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]

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