This weekend, the local Cinema sold a total of 8500 movie tickets. The proceeds totaled $64,600. Tickets can be bought in one of 3 ways a matinee ticket costs $5 student tickets costs $6, and regular tickets are $8.50. How many of each type of ticket was sold if twice as many student tickets were sold as matinee tickets?

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Let x be the number of matinee tickets.

In that case, the number of student tickets is 2x.

The number of regular tickets is (8500-x-2x) = (8500-3x).

Total money

5x + 6*(2x) + 8.50*(8500-3x) = 64600

Simplifying and solving for x

5x + 12x - 8.50*3*x + 8.50*8500 = 64600

5x + 12x - 8.50*3*x = 64600 - 8.50*8500

Solving x , we get

x = 900

Number of matinee tickets = 900

Number of student tickets = 1800

Number of regular tickets = 8500 - (900+1800) = 5800

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