JAN D.

# WHAT QUANTITY OF A 70% ACID SOLUTION HAS TO BE MIXED WITH A 20% ACID SOLUTION TO GET 300ml OF A 45% ACID SOLUTION

WHAT QUANTITY OF A 70% ACID SOLUTION HAS TO BE MIXED WITH A 20% ACID SOLUTION TO GET 300ML OF A 45% SOLUTION?

## 2 Answers By Expert Tutors

By: Motivational tutoring in Science and Math Paul C.

tutor

Kyle,  I like your solution, and I'd like to add a comment that might make it easier for some of us "regular folks" to understand.

Working with concentrations is similar to working with AVERAGES.   We want the mix to average out to 45% concentration in the end.  How many "parts" of 20 do we need, and how many "parts" of 70?  When we AVERAGE, we add together, and divide by the number of inputs.  For example, 20+70=90,  which we then divide by 2, to get 45.   If we add one part of 20% to one part of 70%, and mix them together, they "average" out to 45%.  Since we want to have a total of 300mL in the end, we are going "half and half."  We will use 150 mL of the 70% acid solution, and 150mL of the 20% acid solution.

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10/29/12 Kyle M.

tutor

What confuses me about your explination is that we are not averaging the concentrations in the regular sense, but taking a weighted average of the concentrations to acheive a desired result, which can be significantly harder to conceptulaize.  Although both solutions are weighted the same in this problem, I would not expect every word problem forming a system of equations to do the same.  Also, a second equatiuon must always be formed, in this case expressing the relationship between the weights (x+y=1), forming the general equation Ax+B(1-x)=C for two solutions with concentrations A and B and resulting solution with concentration C.  Furthermore, once the student has solved for the value of the weight, he or she would have to go back to solve for the ammount of liquid needed from each solution, which wouldn't be dificult, but would require again, an understanding of weighted averages.  I beleive the explination I propose offers a little more insight into forming a system of equations.  But I understand that my explination can be seen as 'removed' from the average person and I apreciate the simplicity in your explination.

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10/29/12 