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
