Catseyeglint911
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How much of a 60% acid solution must be mixed with 50 gallons of a 24% acid solution to obtain a solution that is 50% acid?
a. 130 gal
c. 13 gal
b. 125 gal
d. None of these
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JoannaBlackwelder
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I would use the idea of a mass balance of the acid.
JoannaBlackwelder
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For example, the amount of acid in the 50 gallons of a 24% acid solution would be 50*.24=12 gallons of acid.
JoannaBlackwelder
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Make sense so far?
Catseyeglint911
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yes
JoannaBlackwelder
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Sweet. Since we don't have the volume of the 60% acid solution, I will call that x.
JoannaBlackwelder
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Can you write an expression that shows the volume of acid of the 60% acid solution?
Catseyeglint911
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0.5 = 0.6x + (50*0.24)
I have a feeling that this isn't right.
JoannaBlackwelder
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That is close. The addition side looks good, but what about the volume of the combined solution?
JoannaBlackwelder
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@Catseyeglint911?
Catseyeglint911
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sorry I had to step a way for a bit
JoannaBlackwelder
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No worries :)
Catseyeglint911
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(0.5*50) = 0.6x + (50*0.24)
Is this what you meant?
JoannaBlackwelder
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Closer. :) The volume of the 24% solution is 50 gals and the 60% acid solution has volume x gals, so wouldn't the combined 50% acid solution have more volume that 50 gals?
Catseyeglint911
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So we would have to use two variables since we don't know the number of gallons need of the 60% solution nor do we know the number of gallons of the final solution?
JoannaBlackwelder
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We could, but we don't have to. Since we know we are adding two volumes together and one volume is 50 gallons and we defined the second volume to be x gallons. So the combined volume is 50+x gallons.
Catseyeglint911
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(x+50) = 0.6 + (50*0.24)
It's still wrong isn't it?
JoannaBlackwelder
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Last time you put (0.5*50) = 0.6x + (50*0.24) which was closer. The only thing you needed to change was (0.5*[50+x]) = 0.6x + (50*0.24)
JoannaBlackwelder
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The 50 to a 50+x
JoannaBlackwelder
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Do you follow me?
Catseyeglint911
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Ooohhh! I see now. :D
JoannaBlackwelder
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Can you solve for x?
Catseyeglint911
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(0.5*[50+x]) = 0.6x + (50*0.24)
25 + 0.5x = 0.6x + 12
13 + 0.5x = 0.6x
13 = 0.1x
130 = x
right?
JoannaBlackwelder
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Awesome! :)
Catseyeglint911
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Thank you so much. :)
JoannaBlackwelder
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No worries