Question

A theater offered pre-sale tickets two days before a showing. On the first day, 12

adult and 5 children's tickets were purchased for $114.50. On the second day, 24
adult and 8 children's tickets were purchased for $218. Find the price of an adult
ticket and a children's ticket.

Answer 1

Adult Ticket is $7.25 and Child Ticket is $5.50

Explanation:

Lets make 2 equations out of the given information.

a = adults

c = children

Equation 1: 12a + 5c = 114.5

Equation 2: 24a + 8c = 218

We can now multiple Equation 1 by 2 so that we are able to eliminate the value of a.

New Equation 1: 24a + 10c = 229

Equation 2: 24a + 8c = 218

Now we can use subtraction and get a new equation: 2c = 11

Then divide and get: c = 5.5

The cost for a child's or "children's" ticket is $5.50 each. We can fill in the value of the childs ticket and get the value of an adult's ticket as $7.25.

Therefore, Children's Ticket costs: $5.50 & Adult's Ticket costs: $7.25

Answer 2

Adult ticket: $7.25

Children's ticket: $5.50

Explanation:

Set up a system of equations where a represents the cost of an adult ticket and c represents the cost of a child's ticket:

12a + 5c = 114.5

24a + 8c = 218

Solve by elimination by multiplying the top equation by -2:

-24a - 10c = -229

24a + 8c = 218

Add them together:

-2c = -11

c = 5.5

Now, plug in 5.5 as c in an equation to find a:

12a + 5c = 114.5

12a +5(5.5) = 114.5

12a + 27.5 = 114.5

12a = 87

a = 7.25