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tatyana61 [14]
3 years ago
5

A movie theater charges $11.00 for adults, $6.50 for children, and $9.00 for senior citizens. One day the theater sold 405 ticke

ts and collected $3315 in receipts. Twice as many children’s tickets were sold as adult tickets. How many adults, children, and senior citizens went to the theater that day?
Mathematics
1 answer:
Eva8 [605]3 years ago
5 0

Answer: 110 adult, 220 children and 75 senior citizens went to the theater that day.

Step-by-step explanation:

Let x represent the number of adults that went to the theater that day.

Let y represent the number of children that went to the theater that day.

Let z represent the number of senior citizens that went to the theater that day.

One day the theater sold 405 tickets. This means that

x + y + z = 405 - - - - - - - - - - - -1

movie theater charges $11.00 for adults, $6.50 for children, and $9.00 for senior citizens and the total number of receipts that were collected was $3315. This means that

11x + 6.5y + 9z = 3315 - - - - - - - - - -2

Twice as many children’s tickets were sold as adult tickets. This means that

y = 2x

Substituting y = 2x into equation 1 and equation 2, it becomes

x + 2x + z = 405

3x + z = 405 - - - - - - - - - - - - - 3

11x + 6.5 × 2x + 9z = 3315

11x + 13x + 9z = 3315

24x + 9z = 3315 - - - - - - - - - - -4

Multiplying equation 3 by 9 and equation 4 by 1, it becomes

27x + 9z = 3645

24x + 9z = 3315

Subtracting, it becomes

3x = 330

x = 330/3

x = 110

Substituting x = 110 into equation 3, it becomes

3 × 110 + z = 405

330 + z = 405

z = 405 - 330

z = 75

y = 2x = 2 × 110

y = 220

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