To determine Sam's total earnings [tex]\(E\)[/tex] for the day, let's break down his earnings into two parts: his wages and his tips.
1. Calculating his wages:
- Sam earns \[tex]$6 per hour.
- He works for 4 hours on this particular day.
To find his total wages for the day, we multiply his hourly wage by the number of hours worked:
\[
\text{Total wages} = \$[/tex]6 \, \text{per hour} \times 4 \, \text{hours} = \[tex]$24
\]
2. Calculating his tips:
- Sam earns approximately \$[/tex]2.50 in tips for each person he serves.
- Let [tex]\(n\)[/tex] represent the number of people Sam serves that day.
Therefore, the total amount he earns in tips is:
[tex]\[
\text{Total tips} = \$2.50 \times n
\][/tex]
3. Formulating the total earnings:
- To find Sam's total earnings for the day [tex]\(E\)[/tex], we sum his wages and his tips.
Therefore, the function [tex]\(E\)[/tex] which represents his total earnings for the day can be expressed as:
[tex]\[
E(n) = \text{Total wages} + \text{Total tips} = 24 + 2.5n
\][/tex]
4. Choosing the correct option:
From the given options, the correct function that represents Sam's total earnings for the day is:
[tex]\[
\boxed{E(n) = 2.5n + 24}
\][/tex]
Thus, the appropriate choice is Option B: [tex]\(E(n) = 2.5n + 24\)[/tex].
