Sam is a waiter at a local restaurant where he earns wages of $7 per hour. Sam figures that he also earns about $5 in tips for each person he serves. Sam works 6 hours on a particular day.
If $n$ represents the number of people Sam serves that day, which of the following functions could Sam use to figure $E$, his total earnings for the day?
A. $E(n)=7 n+30$
B. $E(n)=5 n$
C. $E(n)=5 n+42
Answer (2)
Calculate Sam's wage earnings: $7/hour * 6 hours = $42.
Calculate Sam's tip earnings: $5/person * n people = $5n.
Calculate Sam's total earnings: Wages + Tips = $42 + $5n.
The function representing Sam's total earnings is E ( n ) = 5 n + 42 .
Explanation
Problem Analysis Let's analyze the problem. Sam earns an hourly wage and tips. We need to find a function that represents his total earnings, E , based on the number of people he serves, n .
Calculating Wage Earnings First, we calculate Sam's earnings from his hourly wage. He earns $7 per hour and works 6 hours, so his wage earnings are: 7 × 6 = 42
Calculating Tip Earnings Next, we calculate Sam's earnings from tips. He earns $5 in tips for each person he serves, and he serves n people, so his tip earnings are: 5 × n = 5 n
Calculating Total Earnings Now, we find Sam's total earnings by adding his wage earnings and his tip earnings: E = 42 + 5 n
So, the function that represents Sam's total earnings is: E ( n ) = 5 n + 42
Identifying the Correct Option Comparing this to the given options, we see that option C matches our function.
Final Answer Therefore, the correct function is E ( n ) = 5 n + 42 .
Examples
Understanding how income varies with effort is crucial in personal finance. For example, if Sam wants to predict his weekly earnings based on the number of customers he serves, he can use the function E ( n ) = 5 n + 42 . If he plans to serve 30 customers, his estimated earnings would be $E(30) = 5(30) + 42 = 150 + 42 = $192. This helps him plan his finances and set goals.
Sam's total earnings can be calculated using the function E ( n ) = 5 n + 42 , where n is the number of people he serves. This accounts for his wage from working 6 hours and his tips from serving customers. Therefore, the correct option is C: E ( n ) = 5 n + 42 .
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