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?

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