Answer: 485 matinee tickets, 7045 regular tickets and 970 student tickets were sold.
Step-by-step explanation:
Let x represent the number of matinee tickets that were sold.
Let y represent the number of regular tickets that were sold.
Let z represent the number of student tickets that were sold.
Last Tuesday regal cinemas sold a total of 8500 movie tickets. It means that
x + y + z = 8500
Tickets can be bought in 3ways :matinee cost $5, students cost $6 all day and regular cost $8. Proceeds totaled $64605. It means that
5x + 8y + 6z = 64605- - - - - - - - -2
if twice as many students tickets were sold as matinee tickets, it means that
z = 2x
Substituting z = 2x into equation 1 and equation 2, it becomes
x + y + 2x = 8500
3x + y = 8500
y = 8500 - 3x - - - - - - - - - 3
5x + 8y + 6 × 2x = 64605
5x + 8y + 12x = 64605
17x + 8y = 64605- - - - - - - - - 4
Substituting equation 3 into equation 4, it becomes
17x + 8(8500 - 3x) = 64605
17x + 68000 - 24x = 64605
17x - 24x = 64605 - 68000
- 7x = - 3395
x = - 3395/-7
x = 485
z = 2x = 2 × 485
z = 970
Substituting x = 485 and z = 970 into equation 1, it becomes
485 + y + 970 = 8500
1455 + y = 8500
y = 8500 - 1455
y = 7045
