Question

The manager of a movie theatre wants to know the number of adults and children who go to the movies. The theatre charges $8.00 for each adult ticker and $4.00 for each child ticket. At a showing where 200 tickets were sold, the theatre collected $1,304.
A) Write a system of equations to represent this situation.
B) How many adult tickets and how many child tickets were sold?
C) If the operating costs totaled $946.00, what is the amount of profit or loss per ticket?

Answer 1

let a = the number of adult tickets sold
let c = the number of children tickets sold

Answer 2

so we know there were 200 sold so.....

a + c = 200

Answer 3

What does our next equation have to do with? (the first one was about how many people attended)

Answer 4

the next equation needs to deal with the profits being made... right?

Answer 5

Good.

each adult ticket cost 8.00 and each child cost 4.00 for a total of $1,304

so

8a + 4c = 1304

Answer 6

then solve for each?

Answer 7

a + c = 200
8a + 4c = 1304

do you know how to solve this system?

Answer 8

9a + 5c = 1504?

Answer 9

The way you do this is to do something to one of the equations to GET RID of one of the variables. I am going to get rid of the a's... so I will need to multiply the first equation by -8 so it cancels with the +8a in the 2nd equation

Answer 10

-8(a + c = 200)
8a + 4c = 1304


-8a - 8c = -1600
8a + 4c = 1304

now add these

Answer 11

-4c = -296?

Answer 12

which means that c = 74?

Answer 13

Yes... so substitute in

a + c = 200
a + 74 = 200
a = 126

Answer 14

Then part c.

They made $1304 by selling tickets. It cost them $946 for movie rights, lights,etc.

so they actually made $1304 - $946 = $358

They sold 200 tickets so they made $358/200 per ticket

which is $1.79 per ticket.

Answer 15

thank you soooooo much! i haven't had to do these since middle school and i've pretty much forgotten how, obviously. /: