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: $
10
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...

Answer 1

Let x = adult price, y = child price.

Part A
2x + 4y = 48
5x + 2y = 64

From the first: x + 2y = 24 → x = 24 − 2y.
Substitute into second:
5(24 − 2y) + 2y = 64
120 − 10y + 2y = 64
−8y = −56 → y = 7
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.
They have $40, so they do not have enough (short by $1).