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

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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**Jai Ganesh****Administrator**- Registered: 2005-06-28
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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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**coolboyx12****Member**- Registered: 2023-03-10
- Posts: 34

Thank you Ganesh.

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

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

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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**coolboyx12****Member**- Registered: 2023-03-10
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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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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 45,517

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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**Bob****Administrator**- Registered: 2010-06-20
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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

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

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

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.

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

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

The revised calculation:

I stand corrected.

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

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

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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