Math Is Fun Forum

knightdrak01

Member

Registered: 2009-12-02

Posts: 13

Reasoning!

All about reasoning questions

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Every problem has a solution and i'm going to find it

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Reasoning!

Hi knightdrak01;

Where are they?

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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.

knightdrak01

Member

Registered: 2009-12-02

Posts: 13

Re: Reasoning!

some hard questions are here!! no algebra!

give u guys a question now....
Uncle Ben is giving sweets to some kids. If each kid receives 8 sweets, 26 sweets remain. If each kid got 12 sweets, Uncle Ben will be 10 sweets short. How many kids are there?

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Every problem has a solution and i'm going to find it

knightdrak01

Member

Registered: 2009-12-02

Posts: 13

Re: Reasoning!

and give me the answer in reasoning form...

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Every problem has a solution and i'm going to find it

knightdrak01

Member

Registered: 2009-12-02

Posts: 13

Re: Reasoning!

here's another one;

A large watermelon weighs 20kg, with 98% of its weight being water. It is left in the sun and some water evaporates so that now only 95% of its weight is water. What does it now weigh?

p.s are u having trouble with the first on?

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Every problem has a solution and i'm going to find it

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Reasoning!

Hi;

Here is trial error reasoning:

1 kid 8 sweets total sweets 34, 1 kid 12 sweets total sweets 22 no good.
2 kids 16 sweets total sweets 42, 2 kids 24 sweets total sweets 32 no good.
3 kids 24 sweets total sweets 50, 3 kids 36 sweets total sweets 42 no good.
4 kids 32 sweets total sweets 58, 4 kids 48 sweets total sweets 58 bingo!

There are 4 kids:

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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.

knightdrak01

Member

Registered: 2009-12-02

Posts: 13

Re: Reasoning!

u sorta got it wrong... wat happened to  the 12 sweets given each....

Last edited by knightdrak01 (2009-12-02 22:00:47)

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Every problem has a solution and i'm going to find it

knightdrak01

Member

Registered: 2009-12-02

Posts: 13

Re: Reasoning!

and i know the answer just testing if u know it... so i know u got it wrong...

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Every problem has a solution and i'm going to find it

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,861

Re: Reasoning!

Hi Bobby and knightdrak01,

Bobby: You added the 10-sweets shortfall instead deducting it.

Here's how I went about it...
-------------------------------------------------------------------------------------------------
Trial and error:

I guessed 10 kids to start with, so...
1. (10 kids x 8 sweets) + 26 sweets = 106 sweets
2. (10 kids x 12 sweets) - 10 sweets = 110 sweets

It's obvious that to end up with the same number of sweets for scenarios 1 & 2 the number of kids has to be reduced from 10, so...
1. (9 kids x 8 sweets) + 26 sweets = 98 sweets
2. (9 kids x 12 sweets) - 10 sweets = 98 sweets

Solved (same number of sweets for each scenario): there are 9 kids.
-------------------------------------------------------------------------------------------------
Reasoning strategy (which really is algebra in words, though):

There are two constants:
1. The number of kids.
2. The total number of sweets the kids receive...which is the same for each scenario.

The number of sweets given to each kid in each scenario and the number of sweets over or under Uncle Ben's supply are the variables.

Those variables:
1. The difference between the excess and shortfall quantities is 36: ie, 26 - (-10).
2. The difference between the number of sweets each kid gets is 4: ie, 12 - 8.

Divide the total quantity difference (36) by the difference between the number of sweets each kid gets (4) to find the number of kids: 36 / 4 = 9 kids.
-------------------------------------------------------------------------------------------------
Algebra:

"k" = kids
8k + 26 = 12k - 10
4k = 36
k = 9
So again, there are 9 kids.

Last edited by phrontister (2009-12-03 01:55:52)

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"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

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,861

Re: Reasoning!

Hi knightdrak01,

For the watermelon question I can only come up with a combination of reasoning and trial & error. Someone else may see the reasoning involved, but so far it escapes me.

Here's my thinking on it...

- The 'meat' of the watermelon is a constant 0.4kg: ie, 20 x (100%-98%)
- The watermelon's weight x water content %, + the 0.4kg 'meat' = the watermelon's weight:  originally (20 x 98%) + 0.4kg = 20kg.

The equation's answer must equal the watermelon's weight.

Trial and error:
(19 x 95%) + 0.4 = 18.45 (error)
(18 x 95%) + 0.4 = 17.5 (error)
(17 x 95%) + 0.4 = 16.55 (error)

This shows a constant 0.05kg closing of the gap between the watermelon's weight and the equation's answer, and the imbalance continues until the weight is down to 8kg:

8 x 95% + 0.4 = 8 (true)

Answer: The watermelon now weighs 8kg.

Last edited by phrontister (2009-12-03 01:58:25)

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"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

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Reasoning!

Hi phrontister;

Bobby: You added the 10-sweets shortfall instead deducting it.

Sure did, thanks for finding that.

and i know the answer just testing if u know it... so i know u got it wrong...

Why are you not posting these in Exercises instead of Help Me if you already know the answer. Help Me is for people who need help on a problem sometimes quickly.

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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.

soroban

Member

Registered: 2007-03-09

Posts: 452

Re: Reasoning!

Uncle Ben is giving sweets to some kids.
If each kid receives 8 sweets, 26 sweets remain.
If each kid got 12 sweets, Uncle Ben will be 10 sweets short.
How many kids are there?

.

soroban

Member

Registered: 2007-03-09

Posts: 452

Re: Reasoning!

A large watermelon weighs 20kg, with 98% of its weight being water.
It is left in the sun and some water evaporates so that now only 95% of its weight is water.
What does it now weigh?

. .

. .

. .

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

BTW, what's all this trial-and-error stuff?

I thought this was a MATH site!
.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Reasoning!

Hi soroban;

BTW, what's all this trial-and-error stuff?

I thought this was a MATH site!

Look at post #3

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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.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,861

Re: Reasoning!

Look at post #3

And post #4...and the thread title.

The OED's definition of reasoning: To think in a connected, sensible, or logical manner; to employ the faculty of reason in forming conclusions.

I can't do any of that, so I'm not going to be of much help here!

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"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

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Reasoning!

Hi phrontister;

You did good. Actually I wanted to solve it algebraically like soroban did. His requirement of no algebra!!!!!! So befuddled me I didn't even read the question correctly.

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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.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,861

Re: Reasoning!

Hi Bobby,

Actually I wanted to solve it algebraically like soroban did.

Likewise! I didn't know how to go about it with the reasoning/no algebra requirement. You don't have to look too hard at my reasoning strategy in post #9 to work out it's just a rewording of my algebraic strategy in that same post.

I'll be interested to see if knightdrak01 knows the reasoning strategy (not just the answer), and how that differs from algebraic reasoning. I wonder if these two strategies are merely a rewording of each other...for these problems, anyway.

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"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

knightdrak01

Member

Registered: 2009-12-02

Posts: 13

Re: Reasoning!

wow phrontister is really smart.. btw i know the answer but don't know how to do it... bobby...

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Every problem has a solution and i'm going to find it

knightdrak01

Member

Registered: 2009-12-02

Posts: 13

Re: Reasoning!

well i would have done ur way phron... difference between the +26 and - 10 (+26 is the 26 sweets left and -10 is for the 10 sweetes short) then find the difference between 12 and 8 to find the difference of how much is given out. then divide it...

and algebra uses variables while reasoning uses words in stead of variables.. reasoning is much simpler than algebra.. for wat i say..

p.s the watermelon one really helped thanks i didn't know how to do that but i knew the answer

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Every problem has a solution and i'm going to find it

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,861

Re: Reasoning!

Hi knightdrak01,

wow phrontister is really smart...

Nah...I'm not even in the same ball park as bobbym and soroban! I just have a go at some of the easier stuff that doesn't require advanced maths knowledge.

No doubt the setter of your two problems has a juicy eye-opening solution for each...ones that I'm struggling to find. I'm often amazed at the clever strategies used by others in their solutions to tricky brain-teasers!

That's one of the reasons maths is fun!

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"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

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Reasoning!

wow phrontister is really smart...

I have no problem with that. Phrontistery means a thinking place.

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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.