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.`
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?
@Nnesha
@Kainui
Do you know how to set up the equation for it?
no
@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 ≥ _____________
ok
Okay, the next part is they have planned to spend 2,500 so you can end up subtracting that from your total..
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 :(
how far did you get?
Not very far @phi
what number do you have to find in this problem ?
What do you mean?
you have to "solve" for something. what is it ?
how much should the full price admission ticket should be charged?
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 ?
if they sell 500 full-price tickets, any idea how much money that is ?
no
we don't know how much money one ticket costs
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 ?
500x ?
yes, 500 times x or 500x now for kid's tickets. How much does a kid ticket cost ? any idea ?
but for the ones who are <12 yrs would be 2x and there's 200 admission tickets for them. so will it be 400x?
almost. but think more about what they say about the cost of a kid's ticket
"Full-price admission tickets will cost twice as much as tickets for visitors who are under 12 years old."
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?
yes
how much does a kid's ticket cost ?
2 kid tickets cost as much as 1 full price ticket
the idea is 1 kid ticket is half of a full price ticket
can we consider the full price ticket to cost 500x?
that is the cost of 500 full-price tickets one is just x
i don't understand.
Be more imaginative. one kid is ½ of full price full price is "x" how do you show ½ of x ?
x/2
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)
but to continue. the kid ticket costs x/2 dollars you sell 200 of them how much money is that ?
100?
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?
200k?
ok, but k is x/2
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
so do you mean to say 200x/2 ?
yes. you can write it a few different ways it does simplify
\[ 200 \cdot \frac{x}{2} = \frac{200x}{2} = 100x\]
so far you found they will get 500x for the full-price tickets 100x for the half-price
so i just want to review how we got to the kid's ticket
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)
ok and then?
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"
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)
If that is hard to follow, that means you have to practice learning how to do that.
okay got it. so would we have this so far 100x + 500x = ___ ?
what would ___ be ?
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
okay so it would now be 600x - 2500 = 5000 ?
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.
now it's algebra. Can you do the algebra to solve for x ?
so it would be x \(\ge\) 12.50
yes, and the minimum x is 12.50
thank you. can you help me on a couple more please?
ok
I mentioned you.
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