Question

#3: The Hansen family bought 2 child and 2 adult movie tickets and paid $36.50. The Owens family bought 5 child and 2 adult tickets and paid $60.50. How much does a child movie ticket cost? *

Answer 1

Cost of child movie = x = $8

Cost of adult movie = y = $10.25

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.

`2x+2y=36.50`

Owens family bought 5 child and 2 adult tickets and paid $60.50.
`5x+2y=60.50`

Let:

`2x+2y=36.50--eq(1)\\5x+2y=60.50--eq(2)`

Subtract both equations:

`2x+2y=36.50\\5x+2y=60.50\\- \:\:\: - \:\:\:\:\:\:\:\: -\\--------\\-3x=-24\\x=(-24)/(-3)\\x=8`

So, we get Value of x =8

Now, putting value of x in eq(1) to find value of y

`2x+2y=36.50\\Put \: x=8\\2(8)+2y=36.50\\2y=36.50-16\\2y=20.5\\y=(20.5)/(2)\\y=10.25`

So, we get Value of y = 10.25

So,

Cost of child movie = x = $8

Cost of adult movie = y = $10.25