Question

Question A volleyball team sold raffle tickets to raise money for the upcoming season. They sold three different types of tickets: premium for $10, deluxe for $4, and regular for $2. The total number of tickets sold was 208, and the total amount of money from raffle tickets was $714. If 78 more regular tickets were sold than deluxe tickets, how many premium tickets were sold?​

Answer 1

24 premium tickets were sold.

Explanation:

Let :

Deluxe ticket = x

Regular tickets = x + 78

Premium tickets = y

x + (x + 78) + y = 208

4x + 2(x+78) + 10y = 714

2x + y = 208 - 78

4x + 2x + 156 + 10y = 714

2x + y = 130 - - - - - (1)

6x + 10y = 558 - - - - (2)

Now we can solve the simultaneous equation using elimination method :

From (1)

y = 130 - 2x

Put y = 130 - 2x in (2)

6x + 10(130 - 2x) = 558

6x + 1300 - 20x = 558

- 14x = 558 - 1300

-14x = - 742

x = 742 / 14

x = 53

Put x = 53 in y = 130 - 2x

y = 130 - 2(53)

y = 130 - 106

y = 24