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Mathematics 52 Online
OpenStudy (calculusxy):

A city council hopes to raise $5,000 for the construction of a new skate park by hosting a skateboarding competition. The list below shows how the competition organizers expect to raise money. `The city council expects to sell 200 admission tickets to children under 12 years old.` `The city council expects to sell 500 full-price admission tickets (to visitors who are 12 years or older)` `Full-price admission tickets will cost twice as much as tickets for visitors who are under 12 years old.` `The organizers will spend $2,500 to bring professional skateboarders to the competition.`

OpenStudy (calculusxy):

Which value represents the minimum amount of money the city council should charge for a full-price admission ticket in order to meet its fund-raising goal?

OpenStudy (calculusxy):

@Nnesha

OpenStudy (calculusxy):

@Kainui

OpenStudy (xmissalycatx):

Do you know how to set up the equation for it?

OpenStudy (calculusxy):

no

OpenStudy (calculusxy):

@xMissAlyCatx

OpenStudy (xmissalycatx):

Okay, well let's just look at a couple of the obvious facts first.. We already know that they want to make up to (or more than) $5,000 so that's one part of your equation.. 5,000 ≥ _____________

OpenStudy (calculusxy):

ok

OpenStudy (xmissalycatx):

Okay, the next part is they have planned to spend 2,500 so you can end up subtracting that from your total..

OpenStudy (xmissalycatx):

I'm running out of time to be on here, I have to leave soon. Try to @ some people to come help you I'm sosososo sorry :(

OpenStudy (phi):

how far did you get?

OpenStudy (calculusxy):

Not very far @phi

OpenStudy (phi):

what number do you have to find in this problem ?

OpenStudy (calculusxy):

What do you mean?

OpenStudy (phi):

you have to "solve" for something. what is it ?

OpenStudy (calculusxy):

how much should the full price admission ticket should be charged?

OpenStudy (phi):

ok. that is a good start. you should give that a "name". x is popular x is the amount of a full price ticket. if they sell 500 full-price tickets, any idea how much money that is ?

OpenStudy (phi):

if they sell 500 full-price tickets, any idea how much money that is ?

OpenStudy (calculusxy):

no

OpenStudy (calculusxy):

we don't know how much money one ticket costs

OpenStudy (phi):

not as a number. but we do know it's x (whatever that turns out to be) so assume each ticket costs x dollars how much money do we get for selling 500 of them ?

OpenStudy (calculusxy):

500x ?

OpenStudy (phi):

yes, 500 times x or 500x now for kid's tickets. How much does a kid ticket cost ? any idea ?

OpenStudy (calculusxy):

but for the ones who are <12 yrs would be 2x and there's 200 admission tickets for them. so will it be 400x?

OpenStudy (phi):

almost. but think more about what they say about the cost of a kid's ticket

OpenStudy (calculusxy):

"Full-price admission tickets will cost twice as much as tickets for visitors who are under 12 years old."

OpenStudy (phi):

full price is twice as much as a kid's x (full price) = (is) 2 * kids x=2k x/2 = k can you make sense of what that means?

OpenStudy (calculusxy):

yes

OpenStudy (phi):

how much does a kid's ticket cost ?

OpenStudy (phi):

2 kid tickets cost as much as 1 full price ticket

OpenStudy (phi):

the idea is 1 kid ticket is half of a full price ticket

OpenStudy (calculusxy):

can we consider the full price ticket to cost 500x?

OpenStudy (phi):

that is the cost of 500 full-price tickets one is just x

OpenStudy (calculusxy):

i don't understand.

OpenStudy (phi):

Be more imaginative. one kid is ½ of full price full price is "x" how do you show ½ of x ?

OpenStudy (calculusxy):

x/2

OpenStudy (phi):

yes. now (to see if it makes sense) "Full-price admission tickets will cost twice as much as tickets for visitors who are under 12 years old." full price x = 2* kid's ticket x= 2 * (x/2) that works (left and right sides are equal)

OpenStudy (phi):

but to continue. the kid ticket costs x/2 dollars you sell 200 of them how much money is that ?

OpenStudy (calculusxy):

100?

OpenStudy (phi):

it can't be just a pure number. all you can do is show 200 times the price of a kid's ticket how do you show that?

OpenStudy (calculusxy):

200k?

OpenStudy (phi):

ok, but k is x/2

OpenStudy (phi):

the idea is a kid ticket costs x/2 think of that as a "thing" or a number (ignore that it looks complicated) and if you sell 200 of them, you get 200 * price which is 200 *x/2

OpenStudy (calculusxy):

so do you mean to say 200x/2 ?

OpenStudy (phi):

yes. you can write it a few different ways it does simplify

OpenStudy (phi):

\[ 200 \cdot \frac{x}{2} = \frac{200x}{2} = 100x\]

OpenStudy (phi):

so far you found they will get 500x for the full-price tickets 100x for the half-price

OpenStudy (calculusxy):

so i just want to review how we got to the kid's ticket

OpenStudy (phi):

ok. Part of getting the kid's price is to understand what the sentence "Full-price admission tickets will cost twice as much as tickets for visitors who are under 12 years old." means. When I read that, I translate "Full-price admission tickets will cost" to "x" (because x is the name we give to the price of a full-price ticket)

OpenStudy (calculusxy):

ok and then?

OpenStudy (phi):

so the sentence becomes " x is twice as much as tickets for visitors who are under 12 years old." the whole "tickets for visitors who are under 12 years old." I think of as k or kids ticket cost so I am reading x is twice as much as kids twice as much means 2 times I guess you have to learn that. x is 2*kids or as an equation x = 2k now I want the price of kid's ticket, so I "solve" for k x/2 = k in English that means " full-price divided by 2 is the price of a kid's ticket"

OpenStudy (phi):

finally, if we sell 200 kid's tickets at a cost of x/2 we get 200*x/2 or 100x (which is some dollar amount)

OpenStudy (phi):

If that is hard to follow, that means you have to practice learning how to do that.

OpenStudy (calculusxy):

okay got it. so would we have this so far 100x + 500x = ___ ?

OpenStudy (calculusxy):

what would ___ be ?

OpenStudy (phi):

they get 500x + 100x for selling the tickets they have to pay out 2500 for the skateboarders before they can make any money 500x+100x - 2500 is how much money the make

OpenStudy (calculusxy):

okay so it would now be 600x - 2500 = 5000 ?

OpenStudy (phi):

to be more accurate they want 5000 or more so you would write \[ 600x -2500 \ge 5000\] but the minimum "x" is when they just make 5000 which is how you wrote it.

OpenStudy (phi):

now it's algebra. Can you do the algebra to solve for x ?

OpenStudy (calculusxy):

so it would be x \(\ge\) 12.50

OpenStudy (phi):

yes, and the minimum x is 12.50

OpenStudy (calculusxy):

thank you. can you help me on a couple more please?

OpenStudy (phi):

ok

OpenStudy (calculusxy):

I mentioned you.

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