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#1 2023-03-14 22:07:55

coolboyx12
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Registered: 2023-03-10
Posts: 34

what's the correct answer for this question

2.6 carpenters can make 8 chairs in 10 days, how many days will be required for 10 carpenters to make 16 chairs?

I'd appreciate it if you would help me with this question. ?


It pays to keep an open mind, but not so open your brains fall out. - Carl Sagan.

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#2 2023-03-14 22:20:38

Jai Ganesh
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Registered: 2005-06-28
Posts: 45,517

Re: what's the correct answer for this question

Hi,


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#3 2023-03-14 23:05:14

coolboyx12
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Registered: 2023-03-10
Posts: 34

Re: what's the correct answer for this question

Thank you Ganesh.


It pays to keep an open mind, but not so open your brains fall out. - Carl Sagan.

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#4 2023-03-15 04:09:41

Bob
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Registered: 2010-06-20
Posts: 9,915

Re: what's the correct answer for this question

hi coolboyx12

This is an example of two proprtion questions 'welded' together.  I find it best to just change one thing at a time.

2.6 carpenters can make 8 chairs in 10 days

If we want to still take 10 days we will have to double the number of carpenters.

So ( 2.6 x 2 ) carpenters can make 16 chairs in 10 days

But we have more carpenters to do this.  The ratio of old number to new number is 2.6 x 2 : 10.  More carpenters means less days so this is an inverse proportion.  So the number of days will reduce in the ratio 10 : 2.6 x 2

Thus


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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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#5 2023-03-15 17:59:47

coolboyx12
Member
Registered: 2023-03-10
Posts: 34

Re: what's the correct answer for this question

I'm confused Bob says its 5.2 days and Ganesh says its 1.3 days what's the correct answer.


It pays to keep an open mind, but not so open your brains fall out. - Carl Sagan.

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#6 2023-03-15 18:24:57

Jai Ganesh
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Registered: 2005-06-28
Posts: 45,517

Re: what's the correct answer for this question

Hi,

Always reckon number of men/days/hours/number of items; that is how I did it.


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#7 2023-03-15 21:02:56

Bob
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Registered: 2010-06-20
Posts: 9,915

Re: what's the correct answer for this question

I'll try to make a general formula for this.  First identify the types of proportion.

If you have more carpenters it will take less days so this is inverse proportion.

If you have to make more chairs this will take more days so this is direct proportion.

I'll use these symbols: original carpenters = a; original chairs = b; original days = c

new carpenters = d; new chairs = e.

Change the number of carpenters from a to d. Inverse => multiply by a/d
so new days = c x a/d

Change the number of chairs from b to e.  direct => multiply by e/b
so new days = c x a/d x e/b

In your problem a = 2.6; b = 8; c = 10; d = 10; e = 16

Therefore the new number of days = 10 x 2.6/10 x x 16/8 = 2.6 x 2 = 5.2

If you want to test this, try varying the values of a to e and satisfy yourself that the formula works.

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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#8 2023-03-15 21:17:40

Jai Ganesh
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Registered: 2005-06-28
Posts: 45,517

Re: what's the correct answer for this question

A better picture would emerge now:

Proportions

Ratos.


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#9 2023-03-15 23:28:11

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,794

Re: what's the correct answer for this question

Hi!

I did it like this:

D = original number of production days (10).
Chairs: final 16 is > original 8, resulting in increased production days of:
   (a) D x 16/8.
Carpenters: final 10 is > original 2.6, resulting in reduced production days of (a) x 2.6/10.

The resulting sum:

Sorry, I didn't see the 2 previous posts until now...but I'll post mine anyway. smile

Last edited by phrontister (2023-03-16 00:10:20)


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#10 2023-03-15 23:49:22

Jai Ganesh
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Registered: 2005-06-28
Posts: 45,517

Re: what's the correct answer for this question

The revised calculation:

I stand corrected.


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#11 2023-03-16 00:16:23

coolboyx12
Member
Registered: 2023-03-10
Posts: 34

Re: what's the correct answer for this question

Thanks everybody especially Bob.


It pays to keep an open mind, but not so open your brains fall out. - Carl Sagan.

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