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?

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