SOLUTION: How many quarts of pure antifreeze must be added to 9 quarts of a 50​% antifreeze solution to obtain a 60​% antifreeze​ solution?

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Question 1161169: How many quarts of pure antifreeze must be added to 9 quarts of a 50​% antifreeze solution to obtain a 60​% antifreeze​ solution?
Found 2 solutions by ikleyn, math_helper:
Answer by ikleyn(52788)   (Show Source): You can put this solution on YOUR website!
.

Let Q be that unknown amount of the pure antifreeze to add, under the problem's question.


Then the total antifreeze in the mixture will be  Q + 0.5*9 quarts,

while the total volume of the mixture will be  Q+9 quarts.


Therefore,  the concentration equation is


     = 0.6   (which is 60% concentration).


From the equation,


    Q + 0.5*9 = 0.6*(Q+9),

    Q + 4.5 = 0.6Q + 5.4

    Q - 0.6Q = 5.4 - 4.5

    0.4Q     = 0.9

    Q        =  = 2.25.


ANSWER.  2.25 quarts of the pure antifreeze should be added.


CHECK.   = 0.6.     ! Precisely correct !

Solved.

---------------------

It is a standard and typical mixture word problem.

There is entire bunch of introductory lessons covering various types of mixture problems
    - 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
    - Advanced mixture problems
    - Advanced mixture problem for three alloys
    - Unusual word problem on mixtures
in this site.

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

A convenient place to quickly observe these lessons from a  "bird flight height"  (a top view)  is the last lesson in the list.

Read them and become an expert in solution 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 textbook in the section "Word problems" 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 math_helper(2461)   (Show Source): You can put this solution on YOUR website!


At the start you have:

9 qts of solution, of which 9/2 = 4.5 qts are antifreeze



You want to add x qts of antifreeze (9/2 + x  is the final amount of 

antifreeze) and have the ratio of that to the total solution (9 + x) 

equal to 60% (0.60): 



  



Solve for x = 9/4 = 2.25 qts  

  



Check:  (9/2 + 9/4) / (9 + 9/4) =  (27/4) / (45/4) = 27/45 = 3/5 = 0.60 (ok) 

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