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

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To create a 10-liter solution of 14% acid by mixing a 10% acid solution and a 24% acid solution, two equations must be set up based on the volumes of each solution. Let x represent the volume of the 10% solution, making the volume of the 24% solution equal to 10 - x. The equations derived from the problem state that 0.10x + 0.24(10 - x) = 1.4, representing the total acid concentration in the final mixture. This leads to a system of equations that can be solved to find the required volumes of each acid solution. The discussion also highlights a potential flaw in the question regarding the use of volume versus mass for the calculations.
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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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