Question

in order to develop a more appealing cheeseburger, a franchise uses taste tests with 8 different buns, 7 different cheeses, 3 types of lettuce, and 3 types of tomatoes. if the taste tests were done at one restaurant by one tester who takes 10 minutes to eat each cheeseburger, approximately how long would it take the tester to eat all possible cheeseburgers? hours

Explanation:

Step1: Calculate the number of possible cheeseburgers

By the fundamental counting principle, the number of possible cheeseburgers is the product of the number of choices for each component.
The number of choices for buns is \(n_1 = 8\), for cheeses \(n_2=7\), for lettuce \(n_3 = 3\), and for tomatoes \(n_4=3\).
The total number of cheeseburgers \(N=n_1\times n_2\times n_3\times n_4\)

$$
LATEXBLOCK0
$$

Step2: Calculate the total time in minutes

Since it takes 10 minutes to eat each cheeseburger, the total time \(T\) (in minutes) is \(T = 10\times N\)
Substitute \(N = 504\) into the formula: \(T=10\times504=5040\) minutes

Step3: Convert minutes to hours

Since there are 60 minutes in an hour, the time \(t\) (in hours) is \(t=\frac{T}{60}\)
Substitute \(T = 5040\) into the formula: \(t=\frac{5040}{60}=84\)

Answer:

\(84\)