Question 1182358: How many ounces of a 40% alcohol solution must be mixed with 12 ounces of a 45% alcohol solution to make a 43% alcohol solution?
Found 3 solutions by Boreal, ikleyn, greenestamps:
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! x oz.*0.40 alcohol=0.40x oz pure alcohol
12 oz*0.45 alcohol=5.4 oz pure alcohol
(12+x) oz of 0.43 alcohol final solution is 5.16 +0.43x oz.
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Therefore, 0.40x+5.4=5.16+0.43x
0.03x=0.24
x=8 oz of 40% (3.2 oz pure)
12 oz of 45% (5.4 oz pure)
=20 oz 43% (8.6 oz pure)
Answer by ikleyn(52781)  (Show Source):
You can put this solution on YOUR website! .
Let x be the volume of the 40% alcohol solution to mix, in ounces.
Write the equation for the pure alcohol content in ingredients and in the final mixture
0.4x + 0.45*12 = 0.43*(x+12)
Simplify and solve
0.4x + 0.45*12 = 0.43x + 0.43*12
0.45*12 - 0.43*12 = 0.43x - 0.4x
x =  = 8.
ANSWER. 8 ounces of the 40% alcohol solution should be mixed.
CHECK. I will check for the final concentration
final concentration =  = 0.43. ! Precisely correct !
Solved.
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It is a standard and 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.
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
Here is a non-algebraic method for solving any two-part mixture problem like this. If your mental math is good, you will get to the answer much faster than with formal algebra.
You are starting with some 45% alcohol and adding some 40% alcohol to get 43% alcohol.
Picture that as starting at 45 on a number line and walking towards 40, stopping when you get to 43.
From 45 to 40 is a distance of 5; from 45 to 43 is a distance of 2; so when you stop at 43 you have walked 2/5 of the way from 45 to 40.
That means 2/5 of the mixture is what you are adding.
So the 12 ounces of 45% alcohol you started with is 3/5 of the mixture; since 3/5 of the mixture is 12 ounces, 2/5 of the mixture is 8 ounces.
ANSWER: 8 ounces
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