To solve this problem step-by-step, let's break down the different components of Sam's earnings.
1. Wage Calculation:
- Sam earns a fixed wage per hour. Given that he earns [tex]$\$[/tex]7[tex]$ per hour and works for 6 hours, we can calculate his total wage for the day as follows:
\[
\text{Total wages} = \text{Hourly wage} \times \text{Number of hours worked}
\]
\[
\text{Total wages} = 7 \times 6 = 42
\]
Thus, Sam earns $[/tex]\[tex]$42$[/tex] from his wages alone.
2. Tips Calculation:
- In addition to his hourly wage, Sam earns tips based on the number of people he serves, with each person giving him about [tex]$\$[/tex]5$ in tips. Let [tex]\( n \)[/tex] represent the number of people Sam serves.
[tex]\[
\text{Total tips} = \text{Tips per person} \times \text{Number of people served}
\][/tex]
[tex]\[
\text{Total tips} = 5 \times n = 5n
\][/tex]
3. Total Earnings Calculation:
- Sam’s total earnings ([tex]\( E \)[/tex]) for the day would be the sum of his wages and his tips. Thus:
[tex]\[
E(n) = \text{Total wages} + \text{Total tips}
\][/tex]
[tex]\[
E(n) = 42 + 5n
\][/tex]
Now, let's match this function with the options provided:
A. [tex]\( E(n) = 5n + 42 \)[/tex]
B. [tex]\( E(n) = 5n \)[/tex]
C. [tex]\( E(n) = 7n + 30 \)[/tex]
The correct function that matches our derived equation [tex]\( E(n) = 42 + 5n \)[/tex] is option A: [tex]\( E(n) = 5n + 42 \)[/tex].
Thus, the correct answer is:
A. [tex]\( E(n) = 5n + 42 \)[/tex]
