SOLUTION: Alan wishes to dilute a mixture that is 10% alcohol to one that is 8% alcohol. How much 5% alcohol mixture should he add to 8 L of the 10% mixture?

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Question 1141587: Alan wishes to dilute a mixture that is 10% alcohol to one that is 8% alcohol. How much 5% alcohol mixture should he add to 8 L of the 10% mixture?
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


(1) Using the standard algebraic approach....

8 L of 10%, plus x L of 5%, equals 8% of (8+x) L:

.10%288%29%2B.05%28x%29+=+.08%288%2Bx%29
.8%2B.05x+=+.64%2B.08x
.16+=+.03x
x+=+.16%2F.03+=+16%2F3

ANSWER: 16/3 L, or 5 1/3 L

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A completely different method -- faster and easier, if you understand it....

You are going from 10% towards 5%; you are stopping at 8%.

8 is 2/5 of the way from 10 to 5. (10-8=2; 10-5=5)

That means 2/5 of the mixture is what you are adding; that means 3/5 of the mixture is what you started with; that means the amount you need to add is (2/5)/(3/5) = 2/3 of the amount you started with.

ANSWER: (2/3)*8 = 16/3 L