Question

last tuesday, Regal Cinemas sold a total of 8500 movie tickets. proceeds totaled $64,600. tickets can be bought in one of 3 ways: a matinee admission costs $5, student admission is $6 all day, and regular admissions are $8.50. how many of each type of ticket was sold if twice as many student tickets were sold as matinee tickets?

Answer 1

M + s + r = 8500
5m + 6s + 8.50r = 64600
s = 2m

m + 2m + r = 8500
3m + r = 8500
r = 8500 - 3m

5m + 6(2m) + 8.50(8500 - 3m) = 64600
5m + 12m + 72250 - 25.50m = 64600
-8.50m = 64600 - 72250
-8.50m = -7650
m = -7650 / - 8.50
m = 900 <=== 900 matinee tickets

s = 2m
s = 2(900)
s = 1800 <===1800 student tickets

r = 8500 - 3m
r = 8500 - 3(900)
r = 8500 - 2700
r = 5800 <=== regular