Question

Students and adults purchased tickets for a recent basketball playoff game. All tickets were sold at the

ticket booth—season passes, discounts, etc., were not allowed.
Student tickets cost $5 each, and adult tickets cost $10 each. A total of $4,500 was collected.
700 tickets were sold.
a. Write a system of equations that can be used to find the number of student tickets, s, and the
number of adult tickets, a, that were sold at the playoff game.
b. Assuming that the number of students and adults attending would not change, how much more
money could have been collected at the playoff game if the ticket booth charged students and adults
the same price of $10 per ticket?
c. Assuming that the number of students and adults attending would not change, how much more
money could have been collected at the playoff game if the student price was kept at $5 per ticket
and adults were charged $15 per ticket instead of $10?

Answer 1

a) 5s + 10a = 4500

s+a = 700

b) $2500

c) $1000

Explanation:

a) Let students = s and adult = a

5s + 10a = 4500 -------1

s+a = 700 -------2

Using elimination metthod

Multiply eqn 2 by 5

5s + 10a = 4500

5s + 5a = 3500

Subtracting

5a = 1000

a =200

s = 700- 300= 500

b) if both tickets sell for $10 each

200*10 + 500*10 = $7000

Extra money that would have been made = 7000- 4500 =$2500

c) if s is $5 and a is $15

Tickets sold = 200*15 + 500*5 =$5500

Extra money made = $5500- $4500

= $1000