tickets for the school play cost $3 for students and $6 for adults. The drama club hopes to bring in at least $450 in sales, and the auditorium has 120 seats. Let a represent the number of adult tickets, and let s represent the number of student tickets.
write a system of inequalities representing this situation

Question

tickets for the school play cost $3 for students and $6 for adults. The drama club hopes to bring in at least $450 in sales, and the auditorium has 120 seats. Let a represent the number of adult tickets, and let s represent the number of student tickets. 
write a system of inequalities representing this situation

shreenithaa · Answer

@zepdrix

shreenithaa · Answer

@Amirra_01

zepdrix · Answer

Let's say the number of adult tickets sold is represented by $\large\rm A$
and at the same time we'll represent the number of student tickets sold by $\large\rm S$

shreenithaa · Answer

ok

zepdrix · Answer

A ticket represents a seat.
So the amount of Adult `and` Student tickets must be `less than or equal to` 120,
Because we only have 120 seats.

zepdrix · Answer

Do you understand how to take that fancy sentence I wrote,
and turn it into an equation with A and S? :)

shreenithaa · Answer

is it 
uh....
3s+6a less than or equal to 120
3s+6a more than or equal to 450
???

shreenithaa · Answer

the thing i dont get is... if v find the solution.. 3s and 6a cancel out causing it to be undefined :\

zepdrix · Answer

Hmm I don't know where the 3 and 6 are coming from :o
We're only dealing with the tickets right now, not the prices.

shreenithaa · Answer

3$ for students and 6$ for adults
it says so on the question

zepdrix · Answer

Yes, that information will give us our other equation :)
We were trying to set up the easier one first though.

Which has nothing to do with price, only tickets.

shreenithaa · Answer

ok :)

zepdrix · Answer

`adult tickets` `and` `student tickets` sold must be `less than or equal to` `120` tickets.

shreenithaa · Answer

mmmm ok

zepdrix · Answer

Do you see how that will translate to this?
`A` `+` `S` `<=` `120`

$\rm A+S\le120$

shreenithaa · Answer

yup

shreenithaa · Answer

what about the other inequality?

zepdrix · Answer

So now we're concerned with price.
We want to make AT LEAST 450.
So our inequality is going to face the other direction.
We want the ticket sales to be `greater than or equal to` 450.

shreenithaa · Answer

uh huh

shreenithaa · Answer

is it a+sles than or equal to 450? :\

zepdrix · Answer

If we sell A adult tickets,
and adult tickets are 6 each,
then 6A represents the total adult ticket sales.

We can do similar with student tickets.
We sold S student tickets,
priced at 3 dollars each,
so 3S is the total student ticket sales.

shreenithaa · Answer

i got that

shreenithaa · Answer

:)

shreenithaa · Answer

so... was my inequality right? hmmm?

zepdrix · Answer

no :(

shreenithaa · Answer

oh [[sad]]

shreenithaa · Answer

then what is it?

zepdrix · Answer

I'm gonna repeat what I said a sec ago,
try to create the equation D:

`6A` represents the `total adult ticket sales`.
`3S` represents the `total student ticket sales`.

We want this equation,
`total ticket sales` `greater than or equal to` `450`
we want to sell at least 450 dollars worth of tickets.

`total adult ticket sales` `+` `total student ticket sales` `gte` `450`

Make the equation :U Do itttt

shreenithaa · Answer

hmm....
6a+3s more than or equal to $450 
??? is this right?

zepdrix · Answer

Yes.
So here is our system:
$$\large\rm ~~A+~~S\le120$$$$\large\rm 6A+3S\ge450$$

zepdrix · Answer

Do we only need the equations to finish the problem? :o
oo fun

shreenithaa · Answer

ohhhhh its a+s not 6a +3s
THANK U SOO MUCH

shreenithaa · Answer

i get it now
thank u

zepdrix · Answer

yay team \c:/

shreenithaa · Answer

SOOOOOO MUCH