Question

Students and adults purchased tickets for a recent school play. All tickets were sold at the ticket booth (discounts of any type) were not allowed.

Student tickets cost $8 each, and adult tickets cost $10 each. A total of $1,760 was collected. 200 tickets were sold.

a. Write a system of equations that can model the number of student and adult tickets sold at the ticket booth for the play.

b. Solve the system you create to find the exact number of student tickets sold and adult tickets sold.

c. Assuming that the number of students and adults attending would not change, how much more money could have been collected at the play if the student price was kept at $8 per ticket and adults were charged $15 per ticket instead of $10?

Answer 1

a. (A + S = 200), (8S + 10A = 1760)

b. The school play sold 80 adult tickets, and 120 student tickets.

c. 400$ more would have been collected if the school charged 15$ per ticket instead of 10$

Explanation:

a. To begin with, we can refer to S as student tickets, and A as adult tickets. We know that 200 tickets were sold, so we can say that (A + S = 200). We can also say that (8S + 10A = 1760).

b. We can twist the first system of equations and put one variable on the other side. It'll be (A = 200 - S). From there, we will substitute A in the second system of equations. The equation will be

(8S + 10(200 - S) = 1760)

Then you solve for S

(8S + 2000 - 10S = 1760)

-2S = -240

S = 120

Substitute for S in the first system of equations

A = 200 - 120

A = 80

or the second

8(120) + 10A = 1760

960 + 10A = 1760

10A = 800

A = 80

This means that the school play sold 80 adult tickets, and 120 student tickets.

c. (8S + 15A = X)

8(120) + 15(80) = X

X = 2160

2160 - 1760 = 400

400$ more would have been collected if the school charged 15$ per ticket instead of 10$