Answer:
Cost of child movie = x = $8
Cost of adult movie = y = $10.25
Step-by-step explanation:
Let cost of child movie = x
Cost of adult movie = y
Now converting statements into mathematical expressions:
Hansen family bought 2 child and 2 adult movie tickets and paid $36.50.
[tex]2x+2y=36.50[/tex]
Owens family bought 5 child and 2 adult tickets and paid $60.50. [tex]5x+2y=60.50[/tex]
Let:
[tex]2x+2y=36.50--eq(1)\\5x+2y=60.50--eq(2)[/tex]
Subtract both equations:
[tex]2x+2y=36.50\\5x+2y=60.50\\- \:\:\: - \:\:\:\:\:\:\:\: -\\--------\\-3x=-24\\x=\frac{-24}{-3}\\x=8[/tex]
So, we get Value of x =8
Now, putting value of x in eq(1) to find value of y
[tex]2x+2y=36.50\\Put \: x=8\\2(8)+2y=36.50\\2y=36.50-16\\2y=20.5\\y=\frac{20.5}{2}\\y=10.25[/tex]
So, we get Value of y = 10.25
So,
Cost of child movie = x = $8
Cost of adult movie = y = $10.25
