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October 9th, 2018, 03:09 AM   #1
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What is the percentage of milk in the resultant mixture?

33.3 litres of a mixture containing 43% milk is mixed with 55.5 lit of one containing 59% milk. What is the percentage of milk in the resultant mixture?

Answer is 53%.

I can take ratio of 33.3/55.5 i.e 3:5

After that, how to proceed the solution?
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October 9th, 2018, 03:45 AM   #2
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Writing 3:5 as 0.6, and the given percentages as 0.43 and 0.59,
you need to find (0.43 × 0.6 + 0.59)/(0.6 + 1), which simplifies to exactly 0.53.

Hence the answer is 53%.
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October 9th, 2018, 04:02 AM   #3
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Quote:
Originally Posted by skipjack View Post
you need to find (0.43 × 0.6 + 0.59)/(0.6 + 1), which simplifies to exactly 0.53.
What formula have you used to calculated?
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October 9th, 2018, 05:05 AM   #4
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......a @ u%
......b @ v%
--------------
(a+b) @ w%

w = (au + bv) / (a + b)
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October 9th, 2018, 05:29 AM   #5
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An equivalent equation is w = ((a/b)u + v)/(a/b + 1), which is what I used.
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October 9th, 2018, 05:34 AM   #6
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Mine is shorter and simpler
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October 9th, 2018, 06:56 AM   #7
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In general, yes. For the posted problem, the evaluation of the formula happens to be easier to do when using the longer formula, because a/b = 0.6, which is rather convenient for mental arithmetic.
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October 9th, 2018, 07:33 AM   #8
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Why memorize a 2nd formula in case ratio is an "easy division"?
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October 9th, 2018, 08:21 AM   #9
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I didn't suggest memorizing it. I used it because I realized it would be easier.
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October 9th, 2018, 08:29 AM   #10
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Not important...just fooling around...
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