SOLUTION: You need a 65% alcohol solution. On hand, you have a 390 mL of a 10% alcohol mixture. You also have 95% alcohol mixture. How much of the 95% mixture will you need to add to obtain

Question 1098393: You need a 65% alcohol solution. On hand, you have a 390 mL of a 10% alcohol mixture. You also have 95% alcohol mixture. How much of the 95% mixture will you need to add to obtain the desired solution?
You will need how much of
of the 95% solution
and how much of the desired 65% solution.
Found 4 solutions by ikleyn, amalm06, greenestamps, richwmiller:
Answer by ikleyn(52782)   (Show Source): You can put this solution on YOUR website!
.

Let x be amount (the volume in mL) of the 95% mixture, which is under the question. Then the "concentration" equation is = 0.65. To solve it, multiply both sides by (390+x). You will get 0.1*390 + 0.95x = 0.65*(390+x). ====> Multiply both sides by 100: 10*390 + 95x = 65*(390+x). ====> 10*390 + 95x = 65*390 + 65x ====> 95x - 65x = 65*390 - 10*390 ====> 30x = 55*390 ====> x = {{(55*390)/30) = 55*13 = 715. Answer. 715 mL of the 95% alcohol solution is needed. You will obtain 715+390 = 1150 mL of the 65% alcohol solution.

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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
in this site.

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 amalm06(224)   (Show Source): You can put this solution on YOUR website!
0.95x+(0.10)(390)=(390+x)(0.65)
0.95x+39=253.5+0.65x
214.5=0.30x
x=715 mL (Answer)
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

Again to tutor ikleyn...

In response to another similar problem, you scolded tutor amalm06 for using a method that you did not understand, saying that students will not understand what they are doing if they use that method.

Yet here in your response to this question, you say the way to start the problem is with the "concentration" equation.

That might be where you would start, probably because of your background in science. But to a beginning student, that is a "magic" formula, the basis of which is not clear.

If you want to advocate using problem solving methods that are easy to understand, then starting working on this problem with a magic formula is not a good way to go.

The standard algebraic approach to the problem is a much better place to start for beginning students. Tutor amalm06 posted a very neat and concise solution for this problem that requires far less work than your method.

And, as I stated in my other recent comment to you, the method of alligation is the most efficient method for solving a problem like this, requiring far less work than the solution you show.
Answer by richwmiller(17219)   (Show Source): You can put this solution on YOUR website!
Oops a typo.
"You will obtain 715+390 = 1150 mL of the 65% alcohol solution."
should read
"You will obtain 715+390 = 1105 mL of the 65% alcohol solution."

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