Please Help (inequalities)

[Antcap5]

Hello im having trouble finding the correct inequalities for this word problem could someone help.
You are trying to find the best way to get the whole senior class from New High School to Gillette Stadium for prom. You have a budget of $8000 to get all 415 students there. The bus company charges $750 for each bus per night, while the van company only charges $400 per night, including the driver. The van company has a minimum requirement of renting 3 vans. Each bus can comfortably fit 45 students while each van can fit 19 students. You also need chaperones in each vehicle, only one chaperone for the van and three chaperones for the bus. Each chaperone gets a free meal at prom, so how many of each vehicle should you order if you want to minimize the number of chaperones?

 

[tkhunny]

Okay, show us the trouble you are having? What have you tried?

 

[Steven G]

Welcome to the forum!
This is a free math help forum and not a free homework service forum.
Please re-read the forum guidelines and post back following the guidelines.
We mainly wan to see your attempt at solving this problem even if you are sure that it is wrong. Seeing your attempt shows us what method you want to use and of course we can then see any errors which you made. Then we can give you expert hints on how to proceed from there.

 

[Antcap5]

Okay, show us the trouble you are having? What have you tried?

I have these inequalitys but im not sure if they are correct because when I graph them they look a little funky 750x+400y<=8000
Y>=3
X>=0
45x+19y<=415

 

[Steven G]

The first thing I would do is to name the unknowns in this problem. What are these unknowns?

 

[Antcap5]

The first thing I would do is to name the unknowns in this problem. What are these unknowns?

Would it be the amount of buses and vans? Sorry, this type of math is fairly new to me

 

[Steven G]

Would it be the amount of buses and vans? Sorry, this type of math is fairly new to me

Yes, very good. Maybe you can let b= the number of buses used and v= number of vans used. Any other unknowns? Can you write some equations/inequalities now?

 

[Antcap5]

Yes, very good. Maybe you can let b= the number of buses used and v= number of vans used. Any other unknowns? Can you write some equations/inequalities now?

Would 750b+400v<=8000
V>=3
45b+19v<=415
B>=0 be the inequalities then?

 

[Steven G]

We defined b and v. Can you now define B and V. Note that b and B are not the same variables. Same with v and V.

 

[Steven G]

I have these inequalitys but im not sure if they are correct because when I graph them they look a little funky 750x+400y<=8000
Y>=3
X>=0
45x+19y<=415

Until you define YOUR variables no one will know if you are correct or not. Don't keep secrets!!

 

[Steven G]

Would 750b+400v<=8000
V>=3
45b+19v<=415
B>=0 be the inequalities then?

Why <=415. What about chaperones??!! Why is v>=3?

 

[Antcap5]

Why <=415. What about chaperones??!! Why is v>=3?

Oops I meant to keep them lowercase. Also I think I messed up shouldnt it be v<=3. Also with the chaperones would they be the objective function. So it would be 1v+3b

 

[Steven G]

Oops I meant to keep them lowercase. Also I think I messed up shouldnt it be v<=3. Also with the chaperones would they be the objective function. So it would be 1v+3b

Why is v<=3?
How can having chaperones not impact the number of available seats?

 

[Antcap5]

Why is v<=3?
How can having chaperones not impact the number of available seats?

Its because you need to rent a minimum of 3 vans

 

[Steven G]

Its because you need to rent a minimum of 3 vans

That is not true at all! Where does it say that you MUST rent 3 vans or 4 vans or.... You can rent 0 vans! I will agree that you can't rent 1 van or 2 vans but will not back down from saying that you can choose to not rent a van.

Also, if you must rent at least three vans then it should be that v>=3, not v<=3. What you claim is that everybody in the world must rent 3 or more vans. Do you see that?

 

[Antcap5]

That is not true at all! Where does it say that you MUST rent 3 vans or 4 vans or.... You can rent 0 vans! I will agree that you can't rent 1 van or 2 vans but will not back down from saying that you can choose to not rent a van.

Also, if you must rent at least three vans then it should be that v>=3, not v<=3. What you claim is that everybody in the world must rent 3 or more vans. Do you see that?

Im very confused sorry. So right now i think the correct inequalities are v>=3, b>=0, 750b+ 400v<=8000. Im still trying to figure out if the last one is 45b+19v>=415 or if its 3b+1v

 

[Steven G]

If v>=3, the v can not be 0. Is it correct to assume that you can't rent 0 vans? The restriction is IF you rent a van you need to rent at least 3. You can decide to rent none. That is an option!