Question

The tickets for a school play cost $8 for adults and $5 for students. The organizers of the school must make at least $3000 to cover the cost of the set construction, costumes, and programs.

A. Write a system of linear inequalities for the number of each type of ticket sold.


C. If the organizers sell out and sell twice as many student tickets as adult tickets, can they reach their goal? Explain how you got your answer.

Answer 1

Explanation:

Let x represents the number of adult tickets

Let y represents the number of student tickets

x + y ≤ 525

8x + 5y ≤ 3000

(C)

x + y ≤ 525

8x + 5y ≤ 3000

y = 525 - x

substituting y = 525 - x

8x + 5(525 - x) ≤ 3000

8x + 2625 - 5x ≤ 3000

8x - 5x + 2625 ≤ 3000

3x + 2625 ≤ 3000

3x ≤ 3000 - 2625

3x ≤ 3000 - 2625

3x ≤ 375

x ≤ 375 / 3

x ≤ 125

Substitute x ≤ 125 into equation

125 + y ≤ 525

y ≤ 525 - 125

y ≤ 400

For the organizer to meet at most $3000 target;

The number of adult tickets sale must be less than or equal to 125

The number of student tickets sale must be less than or equal to 400

However, these conditions do no give the organizer the assurance they will meet the target, because they need at least $3000 to cover for their expenses.

If the organizer sell out and sell twice as many student tickets as adult tickets.

Then, the new student tickets sale will increase by 2 times adult ticket sale.

Student tickets sale = 400 + (2 x 125)

= 400 + 250

= 650

8(125)+ 5(650) ≤ 3000

1000 + 3750 ≤ 3000

4750 ≤ 3000

This shows the organizers with meet their target of at least $3000