Tickets to a broadway show cost $35 for adults and $10 for children. the total receipts for 1650 tickets at one performance were $41,750. how many adult and how many child tickets were sold?

1010 adult tickets and 640 child tickets were sold

Step-by-step explanation:

Let x represent the number of adult tickets that were sold.

Let y represent the number of child tickets that were sold.

The total number of tickets sold was 1650. This means that

x + y = 1650

Tickets to a Broadway show cost $35 for adults and $10 for children. The total receipts for 1650 tickets at one performance were $41,750. This means that

35x + 10y = 41750 - - - - - - - - - -1

Substituting x = 1650 - y into equation 1, it becomes

35(1650 - y) + 10y = 41750

57750 - 35y + 10y = 41750

- 35y + 10y = 41750 - 57750

- 25y = - 16000

y = - 16000/-25

y = 640

x = 1650 - y = 1650 - 640

x = 1010