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

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