Question

A total of 2500 tickets were sold at a football game. Prices were $2 for children, $3 for students, and $5 for adults. Twice as many tickets were sold to students as children and ticket revenues were $7250. Use a system of linear equations to determine how many of each type of ticket were sold.

Answer 1

1) c + s + a = 2500

2) 2c + 3s + 5a = 7250

3) s = 2c

substitute eq(3) into eqs (1) and (2):

a) c + 2c + a = 2500  or 3c + a = 2500  or a = 2500 - 3c

b) 2c + 3(2c) + 5a = 7250  or  8c + 5a = 7250

substitute eq(a) into eq(b):

8c + 5(2500 - 3c) = 7250

8c + 12,500 - 15c = 7250

-7c = -5250

c = -5250/-7 = 750

using eq(3):

s = 2(750) = 1500

using eq(1):

750 + 1500 + a = 2500

a = 2500 - 2250 = 250

check using eq(2):

2(750) + 3(1500) + 5(250) = 7250

1500 + 4500 + 1250 = 7250

7250 = 7250

There were 250 adult tickets, 1500 student tickets and 750 childrens tickets sold.