Mix 10% & 24% Acid Solution to Make 10 L of 14% Acid

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Discussion Overview

The discussion revolves around a problem involving the mixing of a 10% acid solution with a 24% acid solution to create 10 liters of a 14% acid solution. Participants are attempting to set up the appropriate equations to solve for the volumes of each solution needed.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant suggests the equation a(0.10) + b(0.24) = 10(0.14) to represent the problem, indicating a need to solve for the unknowns a and b, which represent the volumes of the 10% and 24% acid solutions, respectively.
  • Another participant expresses uncertainty about how to approach the problem and requests assistance in setting up the equation to find the necessary volumes.
  • A different participant questions the clarity of the exercise and emphasizes the need to define the units involved, suggesting that the unknowns may represent volumes and noting the condition that their sum must equal 10 liters.
  • It is pointed out that the sum of the volumes of both acids must equal 10 liters, and that the weighted contributions of each solution must equal the concentration of the final mixture, leading to two equations in two unknowns.
  • One participant critiques the problem's formulation, suggesting that using volumes instead of masses could clarify the question.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the clarity of the problem statement, with some expressing confusion and others critiquing the assumptions made regarding units. Multiple viewpoints on how to approach the problem remain present.

Contextual Notes

There is uncertainty regarding the definitions of the units being used (mass per volume vs. volume per volume) and the implications of these definitions on the problem's setup. The discussion also highlights potential issues with the problem's formulation.

imdapolak
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1. You wish to mix 10% acid solution with 24% acid solution to make 10 liters of 14% acid solution. How much of each do you use?


2. a(.10)+b(.24)=10(.14) ? I think the problem is asking for what a and b are , and both added together equal 10 liters at 14% acid solution. The only instructions are to write out an equation for each problem and solve.


3. Hello, this is one problem that I'm not sure how to go about solving this problem. For this section of my mathbook problems such as these involve creating an equation that solves for the solution. I would just like to see how you set up the equation itself in order to solve this problem to find the value of needed liters. Any help is greatly appreciated, thanks.
 
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how do you think you would set up the equation - have to give it a try first...
 
Your exercise b3 is not clear. What is the exercise description and what is the question?

Your exercise b1 forces us to assume your units are either mass per volume or volume per volume; either way, your unknown quantities may well be volumes for the 10% and for the 24% acids. You have in the description the condition that the sum of the volumes should be 10 liters. If x=volume of 10% acid, then the volume of 24% acid must be 10-x. Do you understand the reasoning? (I may have skipped a step). Can you take the solution process further?
 
Sum of volumes of both acids must be 10. 10% of the first volume plus 24% of the second must equal 14% of the final volume. That gives two equations in two unknowns.

Question is faulty, but that's another story. Why do they have to use volumes instead of masses, which will make question perfectly correct?
 

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