Write a system of equations to solve the problem.

Question

A local theatre sells out for their show. They sell all 500 tickets for a total purse of $7,950.00. The tickets were priced at $15 for students, $12 for children, and $18 for adults. If the band sold three times as many adult tickets as children's tickets, how many of each type were sold?

Answer 1

Hello Yazmine,

You can follow these steps to answer the question:

1. We know the theatre sells a total of 500 tickets, so we can write out our first equation:
2. A + C + S = 500
3. where A = adult tickets, C = children tickets, and S = student tickets
4. We also know that each ticket has a price and the total amount was $7950.00, so we can go ahead and write our second equation:
5. 18A + 12C + 15S = 7950
6. Finally, we also know that the theatre sold three times as many adult tickets than children tickets, so our third equation is:
7. A = 3C
8. Since we know that A = 3C, we can substitute it into our first equation and solve for S:
9. 3C + C + S = 500
10. 4C + S = 500
11. S = 500 - 4C
12. Now we can substitute S and A in our second equation and solve for C:
13. 15(500 - 4C) + 12C + 18(3C) = 7950
14. 7500 - 60C + 12C + 54C = 7950
15. 6C = 450
16. C = 75
17. Now that we know that C = 75, we can figure out how many adult tickets were purchased by using our third equation:
18. A = 3 (75)
19. A = 225
20. Finally, we can input A and C values back into the first equation and solve for S:
21. 225 + 75 + S = 500
22. 300 + S = 500
23. S = 200
24. We now have the number of tickets for each type sold:
25. Adult tickets (A) = 225
26. Student tickets (S) = 200
27. Children tickets (C) = 75
28. It's also important to check our work, so let's put these values in our second equation:
29. 18A + 12C + 15S = 7950
30. 18(225) + 12(75) + 15(200) = 7950
31. 4050 + 900 + 3000 = 7950
32. 7950 = 7950
33. Our solution is correct! I hope this works.