Question

A movie theater has a seating capacity of 283 . The theater charges $5.00 for children, $7.00 for students, and $12.00 of adults. There are half as many adults as there are children. If the total ticket sales was $ 2050 , How many children, students, and adults attended? children attended. students attended. adults attended.

Answer 1

c + s + a = 283

5c + 7s + 12a = 2050

a = 1/2c

Substitute this into the first equation for the a and solve for t

1/2c +t+c = 283
3/2c + t = 283
t = 283 - 3/2 c

Use the second equation and substitute for the a and the t and then solve for c

5c + 7(283-3/2c) + 12(1/2c) = 2050

5c + 1981 - 21/2c + 6c = 2050
11c -10 1/2c = 69
1/2 c = 69
c=138

a = 1/2(138) = 69

t = 283 - 3/2(138) = 283 - 207= 76

138 children. 76. Teens. 68 adults

Check:
5(138)+ 7(76) + 12(69) = 690 + 532 + 828 = 2050