Question 1203315
.
The Royal Fruit Company produces two types of fruit drinks. 
The first type is 20% pure fruit juice, and the second type is 70% pure fruit juice. 
The company is attempting to produce a fruit drink that contains 35% pure fruit juice. 
How many pints of each of the two existing types of drink must be used to make 
50 pints of a mixture that is 35% pure fruit juice?
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<pre>
     x     pints  of the 70% juice,
and (50-x) pints  of the 20% juice.


x      pints of the 70% juice contain  0.7x      pints of the pure juice;

(50-x) pints of the 20% juice contain  0.2(50-x) pints of the pure juice.

50 pints of the final mixture contain 0.35*50    pints of the pure juice.


When we chose this presentation of ingredients, x and (50-x) pints, we just provided 
the total volume of the mixture of x + (50-x) = 50 pints.


The only condition which remained and which we should satisfy was to make a balance 
of the pure juice in ingredients and in the final mixture.


So, we write this equation for the pure juice amounts

    0.7x + 0.2*(50-x) = 0.35*50   pints of the pure juice.


Simplify the equation and find x

    0.7x + 10 - 0.2x = 17.5

    0.7x - 0.2x = 17.5 - 10

       0.5x     =  7.5

          x     =  7.5/0.5 = 15  pints.


<U>ANSWER</U>.  15 pints of the  70% juice and (50-15) = 35 pints of the 20% juice.
</pre>

Solved.


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It is a standard and typical mixture problem.


For introductory lessons covering various types of mixture word problems see

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/mixtures/Mixture-problems.lesson>Mixture problems</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/mixtures/More-Mixture-problems.lesson>More Mixture problems</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/mixtures/Solving-typical-mixture-problems.lesson>Solving typical word problems on mixtures for solutions</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/mixtures/Typical-word-problems-on-mixtures-from-the-archive.lesson>Typical word problems on mixtures from the archive</A>

in this site.


You will find there ALL TYPICAL mixture problems with different methods of solutions,
explained at different levels of detalization, &nbsp;from very detailed to very short.


Read them and become an expert in solution mixture word problems.