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#1 2015-06-11 10:58:51

Eve76
Member
Registered: 2015-06-11
Posts: 2

simple logic yet difficult

Help! My son in 4th grade got this question at school..I have forgotten how we did it when I was young. someone pls help me solve it.

3 fishermen went fishing.
fisherman 1 and 2 caught 7 fish
fisherman 2 and 4 caught 9 fish
fisherman 1 and 3 caught 12 fish

How many fish did each fisherman catch.

Thank you.
Eve76

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#2 2015-06-11 11:50:48

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: simple logic yet difficult

There are 4 fisherman?


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.

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#3 2015-06-11 16:52:37

Eve76
Member
Registered: 2015-06-11
Posts: 2

Re: simple logic yet difficult

Hei Bobbym,
Thanks for the answer.. I made a mistake… Fisherman 2 and 3 caught 9 fish.  (Not 2 and 4).
Eve76

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#4 2015-06-11 16:52:49

David
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From: Bumpkinland
Registered: 2014-04-23
Posts: 3,164

Re: simple logic yet difficult

4 fishermen?


His dominion is an everlasting dominion, Which shall not pass away, And His kingdom the one Which shall not be destroyed.

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#5 2015-06-11 17:39:30

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,810

Re: simple logic yet difficult

Hi Ev376, and welcome to the forum!

I'd do it like this:

Name fishermen 1, 2 and 3 as a, b & c respectively.

Write three equations based on your updated info:

1. a + b = 7
2. b + c = 9
3. a + c = 12

Then do some substitutions so that your final equation has only one variable for which to solve. eg,

Start with the first equation:

a + b = 7

Into that equation, substitute for b from equation 2, where b = 9 - c:

a + (9 - c) = 7

Into that equation, substitute for a from equation 3, where a = 12 - c:

(12 - c) + (9 - c) = 7

Then simplify, and solve for c:

12 - c + 9 - c = 7

2c = 14

c = 7

I'm sure you can work out the values of a and b from there. smile


"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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#6 2015-06-12 19:57:21

math9maniac
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From: Tema
Registered: 2015-03-30
Posts: 443

Re: simple logic yet difficult

Hi phrontister;

I love your solution. Much simpler and shorter than what I was doing.

May I ask, the solution works out a, b, c as 5, 2, 7 respectively but I believe that's not actually each's catch.
We should multiply each value by 2 so we have 10, 4, 14. And besides, the three sets of catch (7, 9, 12) adds up to 28. Am I thinking right?

math9maniac


Only a friend tells you your face is dirty.

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#7 2015-06-12 20:41:38

David
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From: Bumpkinland
Registered: 2014-04-23
Posts: 3,164

Re: simple logic yet difficult

Hi, no you don't multiply by two to get 28, the total is not 28. Notice that all the fishermen are mationed twice.


His dominion is an everlasting dominion, Which shall not pass away, And His kingdom the one Which shall not be destroyed.

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#8 2015-06-12 21:00:34

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,810

Re: simple logic yet difficult

Hi math9maniac;

We should multiply each value by 2 so we have 10, 4, 14.

It looks like you're doubling each catch because you see each fisherman appear twice in the list of equations.

...the three sets of catch (7, 9, 12) adds up to 28. Am I thinking right?

Sorry, there's a flaw in your logic.

Fishermen like to stretch the numbers regarding quantity and fish size, so this flaw fits the fishermen story. smile

What you've done has this effect:
eg, if math9maniac has $5, phrontister has $2 and David has $7, then together we have $28.

That would be a very nice way to double our money! Maybe we should all meet up...we'd be very rich very quickly!! smile

Last edited by phrontister (2015-06-12 21:12:54)


"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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#9 2015-06-13 00:26:52

math9maniac
Member
From: Tema
Registered: 2015-03-30
Posts: 443

Re: simple logic yet difficult

Thanks guys, I get it now.   ;-)

I have another problem. I need help understanding Vectors, in a very simple way. Thanks in advance.


Only a friend tells you your face is dirty.

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#10 2015-06-13 00:36:12

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: simple logic yet difficult


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.

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#11 2015-06-13 06:50:20

Bob
Administrator
Registered: 2010-06-20
Posts: 10,052

Re: simple logic yet difficult

Or solve like this:

a + b = 7
b + c = 9
a + c = 12

add up

2a + 2b + 2c = 28  => a + b + c = 14

So c = (a + b + c) - (a + b) = 14 - 7 = 7

and so on.

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 smile

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#12 2015-06-13 06:55:07

math9maniac
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From: Tema
Registered: 2015-03-30
Posts: 443

Re: simple logic yet difficult

Thanks bobbym. Information on vectors is absolutely helpful and very simplified too. Thanks a million.


Only a friend tells you your face is dirty.

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#13 2015-06-13 06:59:22

math9maniac
Member
From: Tema
Registered: 2015-03-30
Posts: 443

Re: simple logic yet difficult

Hello Bob,

Your explanation makes a lot of sense. I guess I didn't entirely understand the question. Now fancy me getting this wrong in a test because of misunderstanding.

By the way, I hope you are doing great.


Only a friend tells you your face is dirty.

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#14 2015-06-13 07:06:37

Bob
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Registered: 2010-06-20
Posts: 10,052

Re: simple logic yet difficult

hi math9maniac

Thanks.  And you can ask about vectors here too.

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 smile

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#15 2015-06-13 10:58:04

math9maniac
Member
From: Tema
Registered: 2015-03-30
Posts: 443

Re: simple logic yet difficult

Of course, Bob. Will certainly do.

I know vectors when represented with lower case letters, are written in bold. Well, since we're not typing with a computer keyboard, we write the vector with a wavy line beneath. Are we doing right?


Only a friend tells you your face is dirty.

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#16 2015-06-13 20:35:48

Bob
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Registered: 2010-06-20
Posts: 10,052

Re: simple logic yet difficult

hi math9maniac

There doesn't seem to be a definite rule about this.  I've seen wavy lines both above and below, straight lines, lines with arrow heads etc.  As long as you have made it clear I'd say any are acceptable.  When this issue came up with an exam board, they said that they would even accept nothing if the question didn't need it.  But if magnitude and direction were required then they would treat no notation as just meaning just magnitude and take away a mark.  Then if the candidate put one of the above to indicate they understood the answer was a vector they would give full marks.

If you look at the Wiki page on mathematical notation, you'll see that lots of mathematical theories have a number of different symbols for the same thing.

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 smile

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#17 2015-06-13 20:50:13

math9maniac
Member
From: Tema
Registered: 2015-03-30
Posts: 443

Re: simple logic yet difficult

Alright Bob. Thanks for explaining.
I was just thinking that everything should follow suit. I guess you've made it clear the notation matters not once the meaning is there.

Is the Cross Product used for 2 dimensional vectors? How do you change a vector from magnitude-bearing form to component or coordinate form?

Many thanks.


Only a friend tells you your face is dirty.

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#18 2015-06-13 21:00:29

zetafunc
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Registered: 2014-05-21
Posts: 2,432
Website

Re: simple logic yet difficult

In the linear algebra courses I've taken, it was common not to use any kind of formatting to distinguish between vectors, matrices, scalars, multilinear forms, etc. it simply became too tedious, and it was obvious from the context what each symbol meant. I personally tend to get more put off by all the decorative notation (especially when they start double-underlining or triple-hatting). As bob bundy said, there isn't any definite rule about this, but when dealing with numerous algebraic objects in the same context, these conventions tend to vanish.

However, if you're using just vectors and scalars, then I think a separate format for vectors would be appropriate.

How do you change a vector from magnitude-bearing form to component or coordinate form?

By 'magnitude-bearing form' I guess you mean a unit vector?

Last edited by zetafunc (2015-06-13 21:02:07)

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#19 2015-06-14 07:55:52

Bob
Administrator
Registered: 2010-06-20
Posts: 10,052

Re: simple logic yet difficult

hi math9maniac

The cross product only works in 3D.

If the vectors are a and b then the cross product is a.b.sin(C) where a and b are the respective magnitudes, C is the angle between them and the direction of the resultant is perpendicular to both a and b.

In 2D there would be no such direction, and in higher dimensions there would be many.

It is useful, for example,  in certain branches of physics (I'd have to look up which).

If a 2D vector is (r, θ) then its components are x = r.cos(θ) and y = r.sin(θ).

And if you know x and y, r =√(x^2+y^2)   and  θ  = invtan(y/x)

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 smile

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#20 2015-06-22 10:37:28

math9maniac
Member
From: Tema
Registered: 2015-03-30
Posts: 443

Re: simple logic yet difficult

Hi all;

           Please accept my sincere apologies. Haven't been online for sometime now since mobile device became malfunctioned. Thanks Bob and zetafunc for your replies. And oh, thanks for your patience as well.


Somebody pleaseeeeeeeee pray for me to be, for the first time in my life a proud owner of a personal cell phone (no matter how obsolete it may be). Or is anyone ready to buy me one or hand over an old one that is no longer in use. (Should have Internet access of course). Fancy me: a beggar with a choice.

Seriously I have no choice but to beg (pls forgive me for that). I'm helpless and hopeless and I need your help.


Only a friend tells you your face is dirty.

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#21 2015-06-22 10:41:53

math9maniac
Member
From: Tema
Registered: 2015-03-30
Posts: 443

Re: simple logic yet difficult

Ok Bob, thanks to you and others like bobbym and company, I'm glad to announce that I scored 93 per cent in the mini Math test of which a greater part was Vectors. Now I must prepare for the major exam which is three weeks away. I think I'm scared and not actually ready for that one.


Only a friend tells you your face is dirty.

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#22 2015-06-22 11:38:38

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: simple logic yet difficult

93%! Very good!


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.

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#23 2015-06-22 19:44:48

Bob
Administrator
Registered: 2010-06-20
Posts: 10,052

Re: simple logic yet difficult

hi math9maniac

Well done for the maths mark.

Cell phone ?  I don't even have one of those, so I'm afraid I cannot help.

Major exam ?  Do you have a list of topics you want to practise ?

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 smile

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#24 2015-06-23 05:44:48

math9maniac
Member
From: Tema
Registered: 2015-03-30
Posts: 443

Re: simple logic yet difficult

Seriously Bob, you don't have a cell phone? So how do you get in touch with friends and family?

About the topics I want to practise, I'm going out and won't be back until about 4 hours later. Will send the topics when I return.

Thanks a lot for your help. Cheers.


Only a friend tells you your face is dirty.

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#25 2015-06-23 06:14:43

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,974
Website

Re: simple logic yet difficult

Bob can send encrypted messages to Alice. He does not find cellular networks secure.


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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