SOLUTION: A pharmacist wishes to mix a solution that is 5​% Minoxidil. She has on hand 70 ml of a 2​% solution and wishes to add some 7​% solution to obtain the desired 5&

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Question 1122261: A pharmacist wishes to mix a solution that is 5​% Minoxidil. She has on hand 70 ml of a 2​% solution and wishes to add some 7​% solution to obtain the desired 5​% solution. How much 7​% solution should she​ add?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52788)   (Show Source): You can put this solution on YOUR website!
.
Let x = "How much 7% solution should she add".


Your equation is


    pure Minoxidil + pure Minoxidil = total pure Minoxidil.


    0.02*70        + 0.07*x         = 0.05(x + 70).


    ====>            0.07x          = 0.05x + 0.05*70 - 0.02*70


                     0.07x  - 0.05x = 0.05*70 - 0.02*70


                     0.02x          = 0.03*70  ====>  x =  = 105.


Answer.  105 mL of the 7% solution should be added.


Check.   0.02*70 + 0.07*105 = 8.75 pure Minoxidil.


         0.05*(70 + 105) = 8.75 pure Minoxidil.    ! Correct !

Solved.

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Introductory lessons in this site,  covering various types of mixture problems,  are
    - Mixture problems
    - More Mixture problems
    - Solving typical word problems on mixtures for solutions
    - Word problems on mixtures for antifreeze solutions
    - Word problems on mixtures for alloys
    - Typical word problems on mixtures from the archive

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

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Mixture problems".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.


Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


Here is an alternative to the standard algebraic method for solving problems like this. If you are good with some mental arithmetic, this method will get you to the answer much faster and with much less work.

On the other hand, understanding the standard algebraic method is useful in understanding in general how algebra can help you solve problems.

The ratio in which the two ingredients must be mixed is directly related to where the 5% of the mixture lies between the 2% and 7% of the two ingredients.

One way to picture this is with a number line.

Picture 2, 5, and 7 on a number line. 5 is 3/5 of the way from 2 to 7; that means 3/5 of the mixture needs to be the 7% ingredient.

That means 2/5 of the mixture is the 70ml of the 2% ingredient she starts with. The ratio of 3/5 to 2/5 is 3:2, so the amount of the 7% ingredient she needs to add is 3/2 of 70ml, which is 105ml.
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