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 $ 2.00 for adults and $ 1.00 for students.​ However, this situation has two​ constraints: The theater can hold no more than 150 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:

100 adults and 50 students should attend

and,

The maximum amount raised = $250

Explanation:

Given:

Admission for adults = $2.00

Admission for students = $1.00

Total persons that can be held in theater = 150

For every 2 adults there must be 1 student

let the number of adults be 'x' and the number of students be 'y'

thus,

we can write the above constraints mathematically as:

x + y = 150   ...............(1)

and,

x = 2y  .....(2)  (for 1 student i.e y = 1, there should be 2 adults i.e x = 2 × 1 = 2)

substituting the 'x' from 2 in the equation 1, we get

2y + y = 150

or

y = 50

Thus,

x = 2 × 50 = 100   (from equation 2)

Hence,

100 adults and 50 students should attend

and,

The maximum amount raised = $2 × 100 + $1 ×50 = $250