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last tuesday, Regal Cinemas sold a total of 8000 movie tickets. proceeds totaled $57,000. 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. how many of each type of ticket was sold if twice as many student tickets were sold as matinee tickets?

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kevinbentch

Answer:

The answer is that there were 1000 matinee tickets, 2000 student tickets, and 5000 regular tickets sold.

Step-by-step explanation:

Let m = number of Matinee tickets, s = number of student tickets, and r = number of regular tickets. The sum of these variables is equal to 8000:

m + s + r = 8000

Solve for r:

r = 8000 - m - s

There were twice the number of student tickets as matinee:

s = 2m

Substitute:

m + s + r = 8000

m + 2m + r = 8000

3m + r = 8000

r = 8000 - 3m

The number of each type of ticket sold at that price is equal to the total dollar amount:

5m + 6s + 8r = 57000

Substitute:

5m + 6(2m) + 8(8000 - 3m) = 57000

5m + 12m + 64000 - 24m = 57000

17m - 24m = -7000

-7m = -7000

m = 1000 Matinee tickets sold

s = 2m = 2(1000) = 2000 Student tickets sold

r = 8000 - 3m = 8000 - 3(1000) = 8000 - 3000 = 5000 Regular tickets sold.

Proof total number of tickets:

m + s + r = 8000

1000 + 2000 + 5000 = 8000

8000 = 8000

Proof dollar amount:

5m + 6s + 8r = 57000

5(1000) + 6(2000) + 8(5000) = 57000

5000 + 12000 + 40000 = 57000

17000 + 40000 = 57000

57000 = 57000

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