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Tips and Tricks: Mixtures

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Tips and Tricks: Mixtures [#permalink] New post 30 Apr 2013, 13:45
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Hi guys!

This is my second post of Tips and Tricks, if you have missed the first one be sure to check it out :arrow: Inequalities

In this one I will show you a method (disclamer: I did not invente it :roll: ) to solve easly any mixture problem: it's called Alligation.

It uses a simple table to solve any mixture problem, every answer to such problems can be obtain by looking at this table .

alli.png [ 6.15 KiB | Viewed 4887 times ]

Please note: the X concentration is the highest, the Y is the lowest

The results that you get by subtracting, as I show you in the table, are the ratios of the substances in the desired mixture.

An exmple will explain better than any of my words because this method is really simple to use. I took the following questions from here if you want to get some practice you can try some of those.

1)Seed mixture X is 40 percent ryegrass and 60 percent bluegrass by weight; seed mixture Y is 25 percent ryegrass and 75 percent fescue.
If a mixture of X and Y contains 30 percent ryegrass, what percent of the weight of this mixture is X ?
(A) 10%
(B) 33.33 %
(C) 40%
(D) 50%
(E) 66.66 %

The question asks for the ryegrass so your table should look like this:
all1.png [ 2.28 KiB | Viewed 4885 times ]

Solution: The final raio is\frac{X}{Y}=\frac{5}{10} (or \frac{1}{2}) so for every 1 part of X 2 parts of Y will be in the final mixture
So for a 3 kg mixture (for example)=> 1X and 2Y => X=33% of the total B

This table can be used in other ways also, and this question is an example:
2)How many liters of pure alcohol must be added to a 100-liter solution that is 20 percent alcohol in order to produce a solution that is 25 percent alcohol?
(A) 7/2
(B) 5
(C) 20/3
(D) 8
(E) 39/4

Your table:
all2.png [ 2.4 KiB | Viewed 4883 times ]

Final ratio: \frac{X}{Y} = \frac{5}{75}
We know that Y is 100 liter so \frac{X}{100}=\frac{5}{75} X=\frac{20}{3} C

As you see mixture problems start to look very easy if you consider this method, and for sure all this will save you valuable time 8-)
Hope you guys like it


It is beyond a doubt that all our knowledge that begins with experience.

Kant , Critique of Pure Reason

Tips and tricks: Inequalities , Mixture | Review: MGMAT workshop
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Re: Tips and Tricks: Mixtures [#permalink] New post 02 May 2013, 17:03
Zarrolou-- thanks for showing some new approach !
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Re: Tips and Tricks: Mixtures [#permalink] New post 29 Jun 2014, 06:32
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Re: Tips and Tricks: Mixtures   [#permalink] 29 Jun 2014, 06:32
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