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?

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stokholm stokholm · Answer 1 · 2019-09-10T11:23:17+02:00

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 = [tex]\frac{210}{3} = 70[/tex]

Thus, number of adults attending program = 70 [tex]\times[/tex] 2 = 140

Number of students = 70 [tex]\times[/tex] 1 = 70

Maximum amount = 140 [tex]\times[/tex] $10 + 70 [tex]\times[/tex] $5

= $1,750

Maximum people attending program:

Adult = 140

Student = 70