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**johnphoenix****Member**- Registered: 2013-02-25
- Posts: 10

I have a problem , please help me

A mixture is containing milk and water in the ratio 3:1 . What fraction of the mixture must be replaced by water so that the resultant mixture contains 50% water ?

Please try to explain the steps as well cos I am math at Maths .

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,753

Hi johnphoenix;

If 1 / 3 of the milk was replaced by water then you would have a 50:50 mixture. 1 / 3 of the milk represents 1 / 4 of the mixture, so you must replace 1 / 4 of the mixture.

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**johnphoenix****Member**- Registered: 2013-02-25
- Posts: 10

how is it 1/3 of milk ? Explain please, I am a noob

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,753

Supposing the mixture was divided into 4 pieces. 3 of those pieces are milk, yes?

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**johnphoenix****Member**- Registered: 2013-02-25
- Posts: 10

yeah so milk is 3/4 part of it and water is 1/4 part

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,753

That is right. Take 1 part of the milk ( there are 3 ) and replace it with water. You now have 2 parts milk and 2 parts water. It is 50:50 now.

But 1 part of the milk is only 1 / 4 of the 4 parts of the mixture. So we need to replace 1 part of the mixture which is 1 / 4 of the mixture.

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**johnphoenix****Member**- Registered: 2013-02-25
- Posts: 10

yeah mate , I have understood that but the answer given is 1/3

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,753

Did you copy the question exactly?

**In mathematics, you don't understand things. You just get used to them.**

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**johnphoenix****Member**- Registered: 2013-02-25
- Posts: 10

yes mate ;

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,753

Okay, I thought you just needed some fraction help but you are asking for a mixture problem. I will try and solve that.

**In mathematics, you don't understand things. You just get used to them.**

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**johnphoenix****Member**- Registered: 2013-02-25
- Posts: 10

I guess they want fraction of milk Sorry mate

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**johnphoenix****Member**- Registered: 2013-02-25
- Posts: 10

Got It mate Alligation use allegation 1/3 is correct answer

And ques is exactly quoted

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,753

What is Allegation?

**In mathematics, you don't understand things. You just get used to them.**

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**johnphoenix****Member**- Registered: 2013-02-25
- Posts: 10

Alligation is a method of solving mixture ques.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,753

I agree it is 1 /3 by calculation.

**In mathematics, you don't understand things. You just get used to them.**

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**johnphoenix****Member**- Registered: 2013-02-25
- Posts: 10

Please state the calculation

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,753

Hi;

I soon as I get it, I will post it.

**In mathematics, you don't understand things. You just get used to them.**

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**johnphoenix****Member**- Registered: 2013-02-25
- Posts: 10

ok

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,753

Ley m be the percentage of milk, w be the percentage of water, n is the percentage we must remove.

m = 75

w = 25

n = 1 / 3

The whole 3 equations boil down to this:

*Last edited by bobbym (2013-02-25 07:51:57)*

**In mathematics, you don't understand things. You just get used to them.**

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