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.

Adult ticket: $7.25

Children's ticket: $5.50

Step-by-step 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

the arc length is found by finding the circumference of the full circle (2xpixradius) and then dividing by 4 to find just one quarter of the circle (90 degrees).