## Why and How

For the discussion of math. Duh.

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Ventanator
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### Why and How

Okay, so a friend and I are planning a trip for spring break. I decided that it would be good to have a little equation that shows the relation of people to the price of the trip. I just tried to make one, and being as my math skills are not that great, it (unsuprisingly) failed. I was wondering how I could go about finding the equation, and why mine failed.

Here is what I did:
B is beer, B=(6P*1.2)
T is tubes, T=7P
G is gas, G=40(P/5)
F is food, 5P
P is the number of people.

So, it should (I thought) work so that it comes out M=B+T+G+F, with M being the total price. I should then divide it by the number of people, thus giving the price per person. My final equation was:

M=219.2P/P

I don't know why it's wrong, but it obviously is. I feel that I should know how to do this, seeing as I'm a high school senior. I'm sure it's something simple that I messed up...or I just went about it in horribly the wrong way....Either way, any help would be much appreciated.

Ended
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### Re: Why and How

Did you mistakenly do 40*5 instead of 40/5?

6*1.2 + 7 + 40*5 + 5 = 219.2
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Ventanator
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### Re: Why and How

Would that make it work correctly?

M=27.2P/P
If ten people go, then it would be \$27.2 each, right? But if fifteen go, it would still be be \$27.2. It should be different because there are enough people to need another car, and a whole \$25 more in food. On the same note, if 5 people go, it still comes out to \$27.2.

Does it just increase perfectly so that no matter how many people we bring it will still be \$27.2?

phlip
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### Re: Why and How

Note that all your costs are just (some amount)*P, so if you have twice as many people, the total cost will be twice as much... which split over twice as many people will mean the same cost each.

The whole pool-your-money-and-save thing will only happen if there are some costs that don't go up linearly with P - bulk discounts, or overheads that have a constant cost no matter how many people you have, or that sort of thing.

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Syrin
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### Re: Why and How

Ventanator wrote:It should be different because there are enough people to need another car, and a whole \$25 more in food. On the same note, if 5 people go, it still comes out to \$27.2.

Well, those are concerns that you didn't factor in to your equation.

Yakk
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### Re: Why and How

G is gas, G=40(P/5)

This isn't true. G = 40 * floor((P+4)/5), or so.

If you have 1 person, gas doesn't cost 8\$. It costs 40\$.
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Ventanator
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### Re: Why and How

phlip wrote:The whole pool-your-money-and-save thing will only happen if there are some costs that don't go up linearly with P - bulk discounts, or overheads that have a constant cost no matter how many people you have, or that sort of thing.

Syrin wrote:Well, those are concerns that you didn't factor in to your equation.

Yakk wrote:This isn't true. G = 40 * floor((P+4)/5), or so.

If you have 1 person, gas doesn't cost 8\$. It costs 40\$.

Okay, I definitely feel out of my league. Phlip, I understand what you are saying, but...urgh, okay, so it doesn't matter and the cost will always be the same? It makes sense I guess, but feels wrong.

Syrin, yeah, that's what I mean when I say that my math skills are lacking. I don't really know how to put any of that into an equation...and Yakk, that applies to you too, because I honestly don't know what floor is (but I'm going to google it right now.) Anyway, thanks for your help!

edit: I googled floor and didn't understand any of it...I rather feel that my education is lacking...

achan1058
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### Re: Why and How

Ventanator wrote:Okay, I definitely feel out of my league. Phlip, I understand what you are saying, but...urgh, okay, so it doesn't matter and the cost will always be the same? It makes sense I guess, but feels wrong.
Yes for some things, and no for others. Yes for the portions which scales with person, like food, unless you can get a discount by buying bulk with more people. No for things like gas, since the number of people does not correspond to the number of cars directly. In fact, if your car have 5 seats, it costs more per person to carry 6 people than 5, since you need another car.

In short, your model is incorrect.

Ventanator wrote:edit: I googled floor and didn't understand any of it...I rather feel that my education is lacking...
Floor is just writing the number in decimal notation, and removing the stuff after the decimal point. So floor(12.3456) = 12.

mmmcannibalism
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### Re: Why and How

You will only get a reduce in cost per person if the cost of something changes based on how many people buy it. For instance, if a store sells beer with a one dollar discount on the second case two dollar on the third and so on; then as the amount of people increases the beer cost per person decreases.

As another example, if you were hypothetically driving a bus the cost of gas for the trip is a given amount. As the amount of people goes up, each person would need less gas money.
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Ventanator
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### Re: Why and How

achan1058 wrote:
Ventanator wrote:Okay, I definitely feel out of my league. Phlip, I understand what you are saying, but...urgh, okay, so it doesn't matter and the cost will always be the same? It makes sense I guess, but feels wrong.
Yes for some things, and no for others. Yes for the portions which scales with person, like food, unless you can get a discount by buying bulk with more people. No for things like gas, since the number of people does not correspond to the number of cars directly. In fact, if your car have 5 seats, it costs more per person to carry 6 people than 5, since you need another car.

In short, your model is incorrect.

Ventanator wrote:edit: I googled floor and didn't understand any of it...I rather feel that my education is lacking...
Floor is just writing the number in decimal notation, and removing the stuff after the decimal point. So floor(12.3456) = 12.

Okay, that's what I thought at first. I tried to have the car thing: that is (P/5) because there are five people to a car. With forty dollars in gas multiplied by the number of vehicles. So is Yakk's correct? If so, why? I just don't understand the math part, because the 1 person=\$40 and not \$8 part does make sense.

mmmcannibalism
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### Re: Why and How

Gas used divided by number of people will equal gas money per person

Gas will cost the same with 10 people in 2 cars as 20 people in 4 cars; however, if the number of people is not a multiple of 5 there will be a slight increase in cost because one car will be using 5 peoples worth of gas for less then 5 people.

12 people have to pay the same as 15 people, but the payment is spread out more over 15 people. This extra cost lessens as the number of people increases because covering the 3 gaps is spread out over more people.
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DavCrav
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### Re: Why and How

The gas problem is subtle, but the more people who are going, the less that effect is going to be. If you think about it, if one person goes versus two people, the gas money is halved, whereas if twenty-two people go versus twenty-one, the difference isn't very much at all. Basically, for everything apart from gas you buy the same amount per person, and so each person pays 7.2+7+5=19.2 for beer, tubes and food. So each person pays \$19.20 for their stuff, essentially. For the gas, just work out how many cars you need -- round up the number of people to the nearest 5, multiply this by 8, and then divide by the real number of people to get the right answer, the amount of gas money per person -- and add this to the \$19.20.

Example: 13 people. Round up to 15, multiply by 8 to get 120, then divide by 13 to get about 9 or so. Add this to the \$19.20 to get about \$26 per person. It's always going to be about this for over a dozen people. (15 people, you get \$27.20 per person, for 16 people you get \$29.20, and so on.)

You might well be best off to just get \$30 from each person and sort out the odd \$10 at the end.

Ventanator
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Ah, thank you!