Question 1175368
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On the chance that you will understand it, I will solve this problem quickly and easily with logical reasoning and simple mental arithmetic -- without the need to set up and solve an algebraic equation.<br>
If you understand what I am doing in this solution, you will have a quick and easy way to solve a wide variety of 2-part mixture problems.<br>
I'll mix the 30% and 50% solutions first.<br>
Using 3 times as much 50% solution as 30% solution means that, when I mix these two, 3/4 of the mixture will be the 50% acid.
That means the percentage of the mixture will be 3/4 of the way from 30% to 50%.
3/4 of the way from 30% to 50% is 45%.<br>
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NOTE: That's the key to using this method of solving 2-part mixture problems. 3/4 of this mixture being 50% acid and 1/4 being 30% acid means the percentage of the mixture will be 3/4 of the way from 30% to 50%.<br>
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So mixing the 30% and 50% acid results in a mixture that is 45% acid.<br>
Now the problem is mixing that 45% acid solution with the given 15% acid solution to obtain a mixture that is 35% acid.
35% is 2/3 of the way from 15% to 45%
So 2/3 of the final mixture is the 45% acid and 1/3 is the 15% acid.<br>
Now I'm ready to find the amounts of each.<br>
1/3 of the final mixture is the 15% acid.  That's 1/3 of 96 liters, or 32 liters.<br>
The other 2/3 of the mixture, or 64 liters, is the 45% acid, of which 3/4 is the original 50% acid and 1/4 is the original 30% acid.  That makes 48 liters of the 50% acid and 16 liters of the 30% acid.<br>
ANSWERS: 48 liters of 50% acid; 16 liters of 30% acid; 32 liters of 15% acid.<br>
CHECK:
.50(48)+.30(16)+.15(32) = 24+4.8+.48 = 33.6
.35(96) = 33.6<br>