Answer: 330 regular tickets, 46 premium tickets and 64 elite tickets were sold.
Explanation:
Let x represent the number of regular tickets that were sold.
Let y represent the number of premium tickets that were sold.
Let z represent the number of elite tickets that were sold.
The theatre group sold a total of 440 tickets for the show. It means that
x + y + z = 440- - - - - - - - - -1
Each regular ticket cost $5, each premium ticket cost $15, and each elite ticket cost $25. The total amount made from the show was $3940. It means that
5x + 15y + 25z = 3940- - - - - - - - - 2
The number of regular tickets was three times the number of premium and elite tickets combined. It means that
x = 3(y + z)
x = 3y + 3z
Substituting x = 3y + 3z into equation 1 and equation 2, it becomes
3y + 3z + y + z = 440
4y + 4z = 440- - - - - - - - - - - - -3
5(3y + 3z) + 15y + 25z = 3940
15y + 15z + 15y + 25z = 3940
30y + 40z = 3940 - - - - - - - - - - 4
Multiplying equation 3 by 10 and equation 4 by 1, it becomes
40y + 40z = 4400
30y + 40z = 3940
Subtracting, it becomes
10y = 460
y = 460/10
y = 46
Substituting y = 46 into equation 3, it becomes
4 × 46 + 4z = 440
184 + 4z = 440
4z = 440 - 184
4z = 256
z = 256/4
z = 64
x = 3(y + z) = 3(46 + 64)
x = 330