Let's go through the problem step by step to determine which function Sam could use to figure out his total earnings for the day.
1. Hourly Wage Calculation:
Sam earns a wage of [tex]$5 per hour. He works for 6 hours. To find his total earnings from wages, we multiply his hourly wage by the number of hours worked:
\[
\text{Earnings from wages} = 5 \, \text{dollars/hour} \times 6 \, \text{hours} = 30 \, \text{dollars}
\]
2. Tips Calculation:
Sam also earns $[/tex]3 in tips for each person he serves. Let [tex]\( n \)[/tex] represent the number of people Sam serves. To calculate his earnings from tips, we multiply the tips per person by the number of people served:
[tex]\[
\text{Earnings from tips} = 3 \, \text{dollars/person} \times n \, \text{people} = 3n \, \text{dollars}
\][/tex]
3. Total Earnings Calculation:
Sam's total earnings for the day come from both his wages and his tips. Therefore, we add his earnings from wages to his earnings from tips:
[tex]\[
E(n) = \text{Earnings from wages} + \text{Earnings from tips}
\][/tex]
Substituting the values we calculated:
[tex]\[
E(n) = 30 + 3n
\][/tex]
So, the function [tex]\( E(n) = 3n + 30 \)[/tex] correctly represents Sam's total earnings for the day, where [tex]\( n \)[/tex] is the number of people he serves.
Among the given options, the correct function is:
[tex]\[
\boxed{B. \, E(n) = 3n + 30}
\][/tex]
