Math Problem: You have 2 pipes...

[Lord Evermore]

I thought I wouldn't stop till I solved it, but then I managed to remove all but one instance of A and it still didn't work. So now I quit.

I failed various grades of math and algebra. Then for some reason I aced Algebra for about two years and did Pre-Calculus pretty well. But that was, damn, 9 years ago now. And of course I haven't used most of it since.

 

[RandomCoil]

The brute-force search space can be reduced by recognizing that A and B must either both be even numbers or both be odd numbers. This just comes out of both pipe lengths being odd values and the final distance being even.

 

[Daishiki]

hopefully this'll help you guys out. the first step is that the number of A pipes and number of B pipes must add up to a multiple of 10, otherwise the length won't be a nice integer like 212. However, we don't know what multiple of 10 it'll be. So we'll find the largest multiple that it could be. So let's assume the answer consists of only the shortest pipe, A.

212 / 3.9 = 54.358974358974358974358974358974

going by the 3.9a + 5.9b = 212,

assume: a + b = 50

by substitution:
3.9a + 5.9(50-a) = 212
83 = 2x

well that can't be it, since x has to be an integer. so we'll go down from 50 to 40.

assume: a + b = 40

3.9a + 5.9(40-a) = 212
24 = 2a
a = 12

so we got 12 a-pipes and (40-12) = 28 b-pipes.

 

[Chaotic42]

This looks like a max/min problem. I messed with it for a bit, but I got a weird equation and didn't feel like taking the derivative of it.

 

[Mermaidman]

I think we need a second relationship. Are you sure the teacher didn't say that A+B=40?

If we had two equations:
3.9A+5.9B=212
A+B=40

Then it's much easier

 

[BigJ]

Originally posted by: xUCIxDaiSHi
hopefully this'll help you guys out. the first step is that the number of A pipes and number of B pipes must add up to a multiple of 10, otherwise the length won't be a nice integer like 212. However, we don't know what multiple of 10 it'll be. So we'll find the largest multiple that it could be. So let's assume the answer consists of only the shortest pipe, A.

212 / 3.9 = 54.358974358974358974358974358974

going by the 3.9a + 5.9b = 212,

assume: a + b = 50

by substitution:
3.9a + 5.9(50-a) = 212
83 = 2x

well that can't be it, since x has to be an integer. so we'll go down from 50 to 40.

assume: a + b = 40

3.9a + 5.9(40-a) = 212
24 = 2a
a = 12

so we got 12 a-pipes and (40-12) = 28 b-pipes.

:beer:

 

[Chaotic42]

Originally posted by: BigJ
:beer:

That's fine and all, but I think he needs to actually find a formula that works for all numbers. You can't sit there and guess forever.

 

[MercenaryForHire]

Originally posted by: Mermaidman
I think we need a second relationship. Are you sure the teacher didn't say that A+B=40?

If we had two equations:
3.9A+5.9B=212
A+B=40

Then it's much easier

No, it's solvable without it.

I've been sitting on a proof without "guess the integer" as well, but I'd like to see if ndee can do his own damned homework first.

- M4H

 

[BigJ]

Originally posted by: Chaotic42

Originally posted by: BigJ
:beer:

That's fine and all, but I think he needs to actually find a formula that works for all numbers. You can't sit there and guess forever.

Yea but this is the most substantial thing anyone has posted in the thread so far. So I gave him a :beer: for the effort.

 

[MercenaryForHire]

Originally posted by: Chaotic42

Originally posted by: BigJ
:beer:

That's fine and all, but I think he needs to actually find a formula that works for all numbers. You can't sit there and guess forever.

Fine, here's my proof. It's just a rough outline, but I'll clarify anything asked.

-----
3.9A + 5.9B = 212m

Assume that no A-pipes are used. With only B-pipes, you can use 36 and get a length of 212.4m. Since the A-pipes are smaller, you can reduce the length to 212 by substituting them. Also works backwards by starting with the A-pipes and increasing, but I chose this way.

The key is seeing the relation between the pipe lengths. Note that 3.9 is almost 4 and 5.9 is almost 6. Common factor to 12.

3 A-pipes = 11.7
2 B-pipes = 11.8

Every time you remove 2B and add 3A, you lose 0.1m in overall length.

Repeat 4x, and you get 36 - (2x4) = 28 B-pipes, and 0 + (3x4) 12 A-pipes.
-----



Edit - Spelling.

- M4H

 

[Daishiki]

Originally posted by: Chaotic42

Originally posted by: BigJ
:beer:

That's fine and all, but I think he needs to actually find a formula that works for all numbers. You can't sit there and guess forever.

well... there isn't much guess work for this problem. a + b could only be 50 or 40 by the contraints. it had to be a multiple of 10. more than 60 or more would yield too much length. 30 or less wouldn't make the pipe long enough. since it wasn't 50, logically it was 40. if the lengths didn't both have .9 at the end, this problem would have been a different story.

btw: i hope that was a guinness. cheers

 

[MercenaryForHire]

Originally posted by: BigJ

Originally posted by: Chaotic42

Originally posted by: BigJ
:beer:

That's fine and all, but I think he needs to actually find a formula that works for all numbers. You can't sit there and guess forever.

Yea but this is the most substantial thing anyone has posted in the thread so far. So I gave him a :beer: for the effort.

I concur. It's not bulletproof, but if I were a teacher I'd accept it.

:beer:

- M4H

 

[AFB]

Originally posted by: ndee

Originally posted by: MercenaryForHire
My god. What are you in, elementary school?

3.9A + 5.9B = 212

Solve for A and B.

- M4H

OK, what's the 2nd equation smarties!

A + B = C

 

[morkinva]

39 x2 + 59 xy - 2120 x = 0
by Dario Alejandro Alpern

x = 0
y = t

and also:
x = 12 - 59 t
y = 28 + 39 t


The above isn't my solution, is from this page

First, I multiplied both sides by x trying to get a quadratic, so I get:
x(3.9x+5.9y)=x(212)
3.9x^2 + 5.9xy = 212x or
3.9x^2 -212x +5.9y = 0

since his fields dont seem to accept numbers after the decimal point, I multiplied each side by 10

So plug the following numbers into his fields and you get x=12 and y=28. There's got to be an easier way of doing this:

39x^2 -2120x +59xy = 0

 

[ndee]

Originally posted by: MercenaryForHire

Originally posted by: Mermaidman
I think we need a second relationship. Are you sure the teacher didn't say that A+B=40?

If we had two equations:
3.9A+5.9B=212
A+B=40

Then it's much easier

No, it's solvable without it.

I've been sitting on a proof without "guess the integer" as well, but I'd like to see if ndee can do his own damned homework first.

- M4H

As I told you, I got the answers, it's not about solving the problem, it's about the way to get there. I don't grasp that. Told ya you couldn't do it... TARD BOY!

 

[Chaotic42]

Originally posted by: ndee
As I told you, I got the answers, it's not about solving the problem, it's about the way to get there. I don't grasp that. Told ya you couldn't do it... TARD BOY!

Do you have any work you can post? I have no idea how to solve the problem.

 

[TuxDave]

The only second equation I can see is the equation to force A+B a multiple of ten. Otherwise you'll never get an integer sum.

 

[MercenaryForHire]

Originally posted by: ndee

Originally posted by: MercenaryForHire

Originally posted by: Mermaidman
I think we need a second relationship. Are you sure the teacher didn't say that A+B=40?

If we had two equations:
3.9A+5.9B=212
A+B=40

Then it's much easier

No, it's solvable without it.

I've been sitting on a proof without "guess the integer" as well, but I'd like to see if ndee can do his own damned homework first.

- M4H

As I told you, I got the answers, it's not about solving the problem, it's about the way to get there. I don't grasp that. Told ya you couldn't do it... TARD BOY!

Try scrolling up. :roll:

- M4H

 

[tyim]

Originally posted by: MercenaryForHire
Oi.

I have one word for you all. The BS-callers, those insulting my intelligence, and those trying to solve it via conventional algebra. Just one word.

GRAPH.

Thank you.

- M4H

agreed. Graphing takes me about 20 seconds to find the answer, but the graphing tables seem to be technically a form of brute forcing. However, since there are so few possibilities, this seems to be the most simple solution, albeit perhaps not the most elegant.

 

[TuxDave]

M4H has solved it in an elegant manner. WINNAR!

Fine, here's my proof. It's just a rough outline, but I'll clarify anything asked.

-----
3.9A + 5.9B = 212m

Assume that no A-pipes are used. With only B-pipes, you can use 36 and get a length of 212.4m. Since the A-pipes are smaller, you can reduce the length to 212 by substituting them. Also works backwards by starting with the A-pipes and increasing, but I chose this way.

The key is seeing the relation between the pipe lengths. Note that 3.9 is almost 4 and 5.9 is almost 6. Common factor to 12.

3 A-pipes = 11.7
2 B-pipes = 11.8

Every time you remove 2B and add 3A, you lose 0.1m in overall length.

Repeat 4x, and you get 36 - (2x4) = 28 B-pipes, and 0 + (3x4) 12 A-pipes.

 

[RaynorWolfcastle]

First order diophantine equation

 

[konakona]

The problem assumes you WILL get 212 meters by combining 3.9m pipes and 5.9 pipes. 212 meters can be factored out to be 212*4. To remove the decimal part, you need a multiple of ten for the combined number of two types of pipes (i.e., the answer is 12+28=40=4*10). For the problem to be solvable, you are guaranteed to come up with a combination of 3.9A and 5.9B that equals 53. the ratio comes out to be 3:7. multiply both by 4 and you get 12 and 28.

edit : 666 views on the thread

 

[HonkeyDonk]

Originally posted by: ndee

Originally posted by: MercenaryForHire

Originally posted by: Mermaidman
I think we need a second relationship. Are you sure the teacher didn't say that A+B=40?

If we had two equations:
3.9A+5.9B=212
A+B=40

Then it's much easier

No, it's solvable without it.

I've been sitting on a proof without "guess the integer" as well, but I'd like to see if ndee can do his own damned homework first.

- M4H

As I told you, I got the answers, it's not about solving the problem, it's about the way to get there. I don't grasp that. Told ya you couldn't do it... TARD BOY!

Doesn't "solving" = "the way to get there" ?

 

[MercenaryForHire]

Originally posted by: HonkeyDonk

Originally posted by: ndee

Originally posted by: MercenaryForHire

Originally posted by: Mermaidman
I think we need a second relationship. Are you sure the teacher didn't say that A+B=40?

If we had two equations:
3.9A+5.9B=212
A+B=40

Then it's much easier

No, it's solvable without it.

I've been sitting on a proof without "guess the integer" as well, but I'd like to see if ndee can do his own damned homework first.

- M4H

As I told you, I got the answers, it's not about solving the problem, it's about the way to get there. I don't grasp that. Told ya you couldn't do it... TARD BOY!

Doesn't "solving" = "the way to get there" ?

Apparently he sucks at reading as well as math.

- M4H

 

[DrPizza]

Originally posted by: BigJ
Wheres DrPizza when you need him.

I'm right here. I looked at the problem for a few moments... had a brain fart.
For those of you claiming it's an easy problem, other than brute force, it's a difficult problem.
I believe it falls under Diophantine equations... been wayyy too long for me to recall. But, I do recall it's got something to do with relatively prime...

Good luck on the explanation... I'm just taking a time out from writing a paper, otherwise I'd read enough to recall how to do these. BTW, to those claiming these problems are easy, NDEE, why don't you give them a similar problem to solve...

Incidentally (since I'm not reading through all the idiots calling other people idiots in this thread) I'd like to point out that since they both end in .9, to have an integral length, there needs to be a multiple of 10 total pipes. Thus, for those looking for a 2nd equation, you could have A+B=30, A+B=40, A+B=50, etc.


Hmmm... someone above DID provide a link to 1st order Diophantine equations... I followed the link, it all came back to me Well, some of it.

NDee, follow the link
Reasonably simple explanation.