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?

Number of matinee tickets sold = 900

Number of student tickets sold = 1800

Number of regular tickets sold = 5800

Step-by-step explanation:

Given information

Total number of tickets sold = 8500

Total proceeds =  $64,600

Cost of matinee admission = $5

Cost of student admission = $6

Cost of regular admission = $5

Student tickets sold are twice that of matinee admission

Now, let the matinee , student and regular admission are , , and respectively.

according to the given information we can say that

as given in the question that Student tickets sold are twice that of matinee admission, so we can write

as,

Substituting the above value in equation

And write as:

As we have the value of so the value of and will be

and

Hence,

Number of matinee tickets sold = 900

Number of student tickets sold = 1800

Number of regular tickets sold = 5800

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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

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