Math Is Fun Forum

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Balancing Act

Hi;

I was doing something like that up to post #9, when I saw his answer it did not fit my eqautions because his answer uses only 3 on the left. Anyway is this what you are solving:

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Balancing Act

Hi bobbym,

I see 4 weights on each side, I don't understand how you see only 3 weights on the left.

Yes, that's my equation, along with the condition that they are distinct.

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"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Balancing Act

Hi gAr;

It was the only way I thought to get his book solution in post #8.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Balancing Act

Hi,

But you said you got 184 solutions?

And in #14 you wrote

3*9 + 2*5 + 2*8 = 1*7 + 3* 2 + 1*4 + 3* 6 + 6 * 3

It should be

3*9 + 2*5 + 1*12 = 1*7 + 3*2 + 4*9

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"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Balancing Act

Hi;

You have totally different idea than I had. Yours works. One question for the two on the bottom, I see 1* 12, how do you get 4 * 9?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Balancing Act

hi all,

Only just got to this.  I think the rule

A weight that is placed two sections away from the middle will become twice as heavy as a weight that is placed one section away.

is just the 'law of moments'.  I'm with gAr on this one, and I agree with both answers. (#12)

bobbym: Post another of your solutions please and I'll check it again the law.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Balancing Act

Hi,

That's not my idea, that's how torques are to be calculated !

The masses of the sub balances are added.
So in 1*12, 1 is the distance from the fulcrum and 12 is the weight in the sub balance: 8+4
Similarly the 4*9 : 4 is the distance from fulcrum, 9 is the weight 6+3

Hi Bob,

Just saw your post.
Yes, the "law of moments". I keep on forgetting the names!

Last edited by gAr (2011-08-07 22:23:16)

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Balancing Act

Hi;

None of my solutions are correct. I think I got messed up. One more question though, when I solve gAr's equations I get:

This does not coincide with gAr's post #12.

Post #26 is what I used.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Balancing Act

Hi bobbym,

Is it displayed in the right order? a,b,c... ?

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Balancing Act

Hi gAr;

Yes, what did I do wrong?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Balancing Act

hi bobbym

see picture

edit

3d+2b+3a=e+2f+12h

I think you meant 3f

Bob

Last edited by Bob (2011-08-07 22:40:38)

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Balancing Act

Hi bob;

Thanks for the drawing, I think I got it. It looks too simple to make a mistake on but...

Hi gAr;

I still can not genenrate your answers.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Balancing Act

see above edited post

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Balancing Act

Hi all,

2*d = c
g = 2*h
(c+d)+2*b+3*a = e + 3*f + 4*(g+h)

Using first 2 equations, 3rd one is
3*d + 2*b + 3*a = e + 2*f + 12*h

Yes, that's 3f in the last one, sorry about that!
Now you would get it, bobbym.

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Balancing Act

Oh no! Yep, that is it. Yet another stupid blunder!

Thanks bob and gAr, I finally got it!

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Balancing Act

Hi bobbym,

Glad that you got it.
You're welcome!

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Balancing Act

"Glad to be of service"  ...Hitch Hikers Guide to the Galaxy

Bob

Last edited by Bob (2011-08-07 22:48:05)

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Balancing Act

They say it is better medicine to get something wrong and learn then to get 10 problems right.

My brother says I am overdosing!

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.