Question 1204664
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a nurse wants to make 50 ml of a 20% morphine solution. 
she needs to mix 10% morphine solution with 50% morphine solution to make this happen. 
how many ml of each must she mix?
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<pre>
Let x be the the volume of the 50% morphine solution to use, in milliliters.

Then the volume of the 10% solutions of morphine is (50-x) mL,
to make the total volume of 50 mL.


The 50% solution contributes  0.5x mL       of the pure morphine to the final mixture.

The 10% solution contributes  0.1*(50-x) mL of the pure morphine to the final mixture.


So, the total amount of the pure morphine in 50 Ml of the final mixture is

    0.5x + 0.1*(50-x)  milliliters.


We want this amount of the pure morphine provides 20% final solution.
So, we write this equation, which describes it

    {{{(0.5x + 0.1*(50-x))/50}}} = 0.2.


Simplify it by multiplying both sides by 50

    0.5x + 0.1*(50-x) = 0.2*50.


Simplify further and express x

    0.5x + 5 - 0.1x = 10

    0.5x - 0.1x = 10 - 5

        0.4x    =    5

           x    =    5/0.4 = 12.5.


<U>ANSWER</U>.  12.5 mL of the 50% morphine solution and 50-12.5 = 37.5 ml of the 10% morhine solution should be used.

<U>CHECK</U>.   {{{(0.5*12.5 + 0.1*37.5)/50}}} = 0.2, or 20% concentration of the final solution.   ! correct !
</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.