Part A
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. 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...
Part A:
Let's set up the system of equations based on the given information:
2x + 4y = 48
5x + 2y = 64
Now, let's solve the system using any method of our choice. I will use the substitution method:
From the first equation, we can solve for x in terms of y:
2x = 48 - 4y
x = (48 - 4y) / 2
x = 24 - 2y
Now, substitute x = 24 - 2y into the second equation:
5(24 - 2y) + 2y = 64
120 - 10y + 2y = 64
-8y = -56
y = 7
Now, substitute y = 7 back into x = 24 - 2y:
x = 24 - 2(7)
x = 24 - 14
x = 10
Therefore, the adult ticket price is $10 and the child ticket price is $7.
Part B:
For a family of 2 adults and 3 children, the total cost would be:
2($10) + 3($7) = $20 + $21 = $41
Since their budget is only $40, the family does not have enough money to go to the theater.