A theater is presenting a program on drinking and driving for students and their parents or other responsible adults. The proceeds

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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 $ 12.00 for adults and $ 6.00 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?

Hermina Ferry · Accepted Answer

100 adults and 50 students should attendand, The maximum amount raised = $250Explanation: Given:Admission for adults = $2.00Admission for students = $1.00Total persons that can be held in theater = 150For 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 get2y + y = 150ory = 50Thus, x = 2 × 50 = 100   (from equation 2)Hence, 100 adults and 50 students should attendand, The maximum amount raised = $2 × 100 + $1 ×50 = $250

Hermina Ferry · Answer

160 adults and 80 studentsStep-by-step explanation:With the information from the exercise we have the following system of equations:Let x = number of students; y = number of adultsI want to maximize the following:z = 3 * x + 6 * yBut with the following constraintsx + y = 240y / 2

Hermina Ferry · Answer

Maximum people attending programAdult = 140Student = 70Explanation:Provided information,Maximum seating capacity in the theater = 210 peopleFor each pair of adult there must be at-least one student.Thus, maximum revenue can be calculated as follows: Fee for each adult = $10Fee for each student = $5For each combination of two adult and one student revenue = $10 + $10 + $5 = $25Total people in each combination = 3Thus number of combinations possible = Thus, number of adults attending program = 70 2 = 140Number of students = 70 1 = 70Maximum amount = 140 $10 + 70 $5= $1,750Maximum people attending program:Adult = 140Student = 70

Hermina Ferry · Answer

Maximum people attending programAdult = 140Student = 70Explanation:Provided information,Maximum seating capacity in the theater = 210 peopleFor each pair of adult there must be at-least one student.Thus, maximum revenue can be calculated as follows:Fee for each adult = $10Fee for each student = $5For each combination of two adult and one student revenue = $10 + $10 + $5 = $25Total people in each combination = 3Thus number of combinations possible = Thus, number of adults attending program = 70 2 = 140Number of students = 70 1 = 70Maximum amount = 140 $10 + 70 $5= $1,750Maximum people attending program:Adult = 140Student = 70

Jakob Littel

A theater is presenting a program on drinking and driving for students and their parents or other responsible adults. The proceeds

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