Let's break down the problem step-by-step to find the correct function that represents Sam's total earnings, [tex]\( E \)[/tex], for the day.
### Step 1: Calculate Fixed Wages
Sam earns a fixed wage of \[tex]$5 per hour. Since he works for 6 hours on that day, we need to calculate his total fixed wages for the day:
\[ \text{Fixed wages} = 5 \, \text{dollars/hour} \times 6 \, \text{hours} = 30 \, \text{dollars} \]
### Step 2: Calculate Tips
In addition to his fixed wages, Sam earns tips based on the number of people he serves. He earns \$[/tex]3 in tips per person. Let [tex]\( n \)[/tex] represent the number of people Sam serves. Therefore, his total earnings from tips would be:
[tex]\[ \text{Tips} = 3 \, \text{dollars/person} \times n \, \text{people} = 3n \, \text{dollars} \][/tex]
### Step 3: Total Earnings
To find Sam's total earnings for the day, we need to add his fixed wages to his earnings from tips:
[tex]\[ E(n) = \text{Fixed wages} + \text{Tips} \][/tex]
[tex]\[ E(n) = 30 \, \text{dollars} + 3n \, \text{dollars} \][/tex]
Rewriting it in function format, we get:
[tex]\[ E(n) = 3n + 30 \][/tex]
### Final Answer
The equation [tex]\( E(n) = 3n + 30 \)[/tex] correctly combines Sam's fixed wages with his earnings from tips based on the number of people he serves.
So, the correct answer is:
[tex]\[ \boxed{B. \, E(n) = 3n + 30} \][/tex]
