SOLUTION: How much water should be added to 38 ounces of a 25% solution of alcohol to dilute it to a 19% alcohol solution?

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Question 543301: How much water should be added to 38 ounces of a 25% solution of alcohol to dilute it to a 19% alcohol solution?
Found 3 solutions by richwmiller, amalm06, ikleyn:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
.25*38=.19*(x+38)
9.5 = 0.19x+7.22
2.28=0.19x
x=12
add 12 ounces of water

Answer by amalm06(224) About Me  (Show Source):
You can put this solution on YOUR website!
Shortcut: (6/19)(38)=12 oz of water (Answer)

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let w be the water volume to be added, in liquid ounces.


Then the concentration equation is


%280.25%2A38%29%2F%2838%2Bw%29 = 0.19.


The numerator is the pure alcohol volume in the input solution (same as in the resulting solution).


The denominator is the total liquid volume after dilution.


From the equation,

%280.25%2A38%29%2F0.19 = 38+w

0.25*200 = 38 +w  ====>  w = 50 - 38 = 12.


Answer.  12 ounces of water should be added.

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It is typical mixture problem.

For introductory lessons covering various types of mixture word problems see
    - Mixture problems
    - More Mixture problems
    - Solving typical word problems on mixtures for solutions
    - Typical word problems on mixtures from the archive
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.

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.