Question

A theater is presenting a program on drinking and driving for students and their parents or other responsible adults. The proceeds will be donated to a local alcohol information center. Admission is $ 10.00 for adults and $ 5.00 for students.​ However, this situation has two​ constraints: The theater can hold no more than 210 people and for every two​ adults, there must be at least one student. How many adults and students should attend to raise the maximum amount of​ money?

Answer 1

Answer:

Maximum people attending program

Adult = 140

Student = 70

Explanation:

Provided information,

Maximum seating capacity in the theater = 210 people

For each pair of adult there must be at-least one student.

Thus, maximum revenue can be calculated as follows:

Fee for each adult = $10

Fee for each student = $5

For each combination of two adult and one student revenue = $10 + $10 + $5 = $25

Total people in each combination = 3

Thus number of combinations possible = $\frac{210}{3} = 70$

Thus, number of adults attending program = 70 $\times$ 2 = 140

Number of students = 70 $\times$ 1 = 70

Maximum amount = 140 $\times$ $10 + 70 $\times$ $5

= $1,750

Maximum people attending program:

Adult = 140

Student = 70