A theatre group sold a total of 440 tickets for a show, making a total of $3940. Each regular ticket cost $5, each premium ticket cost $15, and each elite ticket cost $25. The number of regular tickets was three times the number of premium and elite tickets combined. How many of each type of ticket were sold

330 regular tickets, 46 premium tickets and 64 elite tickets were sold.

Step-by-step 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