Question

A theater charges x for adult tickets and y for child tickets. Two adult tickets and 4 child tickets cost $48. Five adult tickets and 2 child tickets cost $64.

Part A

Write and solve a system of equations to find the adult and child ticket prices.

adult: $
child: $

Part B

A family of 2 adults and 3 children has a budget of $40. Do they have enough money to go to the theater?


Choose...
Yes
No

Answer 1

Part A

Let x = adult price, y = child price.

System:
2x + 4y = 48
5x + 2y = 64

Solve: from the first, x + 2y = 24 ⇒ x = 24 − 2y.
Substitute: 5(24 − 2y) + 2y = 64 ⇒ 120 − 10y + 2y = 64 ⇒ −8y = −56 ⇒ y = 7.
Then x = 24 − 2(7) = 10.

adult: $10
child: $7

Part B

Cost for 2 adults and 3 children = 2(10) + 3(7) = 20 + 21 = $41. With a $40 budget, they do not have enough.

Answer: No