Question

A theater has 600 tickets to sell for a show. Two hundred twenty-five adult tickets sell at $2 more than the student tickets. All the tickets are sold, for a total of $2,250. What is the price of each type of ticket?

A. Adult tickets sell at $7, and student tickets sell at $5.

B. Adult tickets sell at $6, and student tickets sell at $4.

C. Adult tickets sell at $5, and student tickets sell at $3.

D. Adult tickets sell at $5, and student tickets sell at $7.

Answer 1

Can anyone please help?

Answer 2

Let # of adult tickets be A
Let # of student tickets be S
Adult tickets sell for p
Student tickets sell for p-2 (adult tickets are $2 more than student tickets)

600 tickets total, so A + S = 600
A*p + S*(p-2) = 2250

Solve that by substitution, I think...

Answer 3

You can eliminate at least one answer possibility because the relationship between the price of student and adult tickets is incorrect...

Answer 4

You can also rule out 2 choices by asking how much money would come in if the cheapest tickets were sold for all 600 seats. If that amount > $2250, that obviously can't be the answer.

Answer 5

(but you really should solve the equations!)

Answer 6

ok lets say that x is adults and y is students

you do this x + y = 600

and 225x + 2y =2250

ok we are going to use substitution method

then do y = -x + 600

plug it into the y in the equation 225x + 2y = 2250

it will be 225x + 2(-x +600) = 2250

then 225x + -2x +1200 = 2250

subtract 1200 from both sides 225x + -2x + 1200 -1200 = 2250 -1200

it will be 225x + -2x = 1050

then add the both x's

223x = 1050 so the x will be 4.7 so round it to $5

Answer 7

so we found the x amount now we will find the y amount

Answer 8

no rounding necessary, the problem solves exactly!

Answer 9

Yes I am solving it now, I get it

Answer 10

the y amount is 3

Answer 11

Am I correct

Answer 12

yeah

Answer 13

Thanks a lot!!!

Answer 14

so it is c

Answer 15

225 adult tickets sold at price p
\[225*p + (600-225)*(p-2) = 2250\]\[225p + 375p-750=2250\]\[600p = 3000\]\[p = 5\]
price of adult ticket is 5
price of student ticket is 5-2 = 3

Answer 16

@FriedRice you came up with a funky equation here: 225x + 2y = 2250

Answer 17

no because you are substituting for y so you need to put it and then add -x + 600

Answer 18

but you are right because you are a mentor

Answer 19

what do x and y represent in that equation?

Answer 20

x represents adults and y represents students

Answer 21

it says that in my equation

Answer 22

okay, what do the coefficients represent? 225 and 2

Answer 23

Two hundred twenty-five adult tickets sell at $2 more than the student tickets

Answer 24

ah, but that's not what you have. x is the number of adults, so you can't have 225 in front x! it should be price * count

Answer 25

adult tickets sell for the price of student tickets + $2. so, x*(student price + 2) + y*(student price) = 2250

Answer 26

ohh ok i might have brain farted on that one

Answer 27

we know that x+y=600, so we can substitute (600-x) for y, to give us
x(student price +2) + (600-x)(student price) = 2250

but we already know that x = 225 and y = 600-225, so that becomes
225(student price + 2) + 375(student price) = 2250
225 * sp + 225*2 + 375*sp = 2250
600*sp = 2250-450
600*sp = 1800
sp = 3

Answer 28

adult price = student price + 2 = 3 + 2 = 5

Answer 29

ok thanks for teaching me

Answer 30

it helps sometimes to do problems with the units attached:

3 adults * $5/adult + 2 students * $3/student etc. and make sure that the units come out properly. that would have exposed the faulty equation immediately because you would have had square adults and so on, whereas everyone knows that they are round :-)

Answer 31

I wish I was as smart as you guys

Answer 32

its ok

Answer 33

you will become knowledgeable while you grow up and learn more