SOLUTION: Mr. Grey cloud works in the lab at a pharmaceutical company. He needs to make 24 liters of a 41% acid solution to test a new product. His supplier only ships a 39% and a 42% soluti

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Question 1101792: Mr. Grey cloud works in the lab at a pharmaceutical company. He needs to make 24 liters of a 41% acid solution to test a new product. His supplier only ships a 39% and a 42% solution. Mr. Greycloud decides to make the 41% solution by mixing the 39% solution with the 42% solution. How much of the 39% solution will Mr. Greycloud need to use?
A. 9 L
B. 24 L
C. 8 L
D. 16 L
Found 2 solutions by richwmiller, greenestamps:
Answer by richwmiller(17219)   (Show Source): You can put this solution on YOUR website!
Let A denote the 42% solution and B denote the 39% solution which we have.
Let C denote the 41% solution which we want.
Using the method of alligation.
42         2 2/3*24=16 L of 42% solution
      41            16+8=24 L of 41% solution
39         1 1/3*24=8 L of 39% solution
           3

1= 42 - 41
2= 41 - 39
E.g. There are 2 parts of A plus 1 parts of B
Then 2+1=3 parts total
2/3=0.66666667
0.66666667*24=16
16 L of 42% solution.
24 L-16 L=8 L
8 L of 39% solution.
or
1/3=0.33333333
0.33333333*24=8 L
8 L of 39% solution.
check
0.39 * 8 + 0.42 * 16 = 0.41*24
3.12 + 6.72 = 9.84
9.84 = 9.84
ok
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


The solution by the other tutor is exactly right -- and it uses the BEST and EASIEST method there is for solving mixture problems -- the method of alligation.

The calculations as he shows them look complicated, so let me show you a quick way of thinking of what those calculations are doing. If you can think of mixture problems this way, you will solve them very quickly and with little effort. So here is how to think of this specific problem:

"41 is 2/3 of the way from 39 to 42; therefore 2/3 of the mixture must be the 42% solution"

That one piece of logical analysis takes care of 90% of the work in solving the problem; from there the rest is easy. The amount of 42% solution is 2/3 of the total 24 liters, or 16 liters; the rest -- 1/3 of 24 liters, or 8 liters -- is the 39% solution.
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