
Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion 
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October 9th, 2018, 03:09 AM  #1 
Senior Member Joined: Aug 2014 From: India Posts: 458 Thanks: 1  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? 
October 9th, 2018, 03:45 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,933 Thanks: 2207 
Writing 3:5 as 0.6, and the given percentages as 0.43 and 0.59, you need to find (0.43 Ã— 0.6 + 0.59)/(0.6 + 1), which simplifies to exactly 0.53. Hence the answer is 53%. 
October 9th, 2018, 04:02 AM  #3 
Senior Member Joined: Aug 2014 From: India Posts: 458 Thanks: 1  
October 9th, 2018, 05:05 AM  #4 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038 
......a @ u% ......b @ v%  (a+b) @ w% w = (au + bv) / (a + b) 
October 9th, 2018, 05:29 AM  #5 
Global Moderator Joined: Dec 2006 Posts: 20,933 Thanks: 2207 
An equivalent equation is w = ((a/b)u + v)/(a/b + 1), which is what I used.

October 9th, 2018, 05:34 AM  #6 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038 
Mine is shorter and simpler 
October 9th, 2018, 06:56 AM  #7 
Global Moderator Joined: Dec 2006 Posts: 20,933 Thanks: 2207 
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.

October 9th, 2018, 07:33 AM  #8 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038 
Why memorize a 2nd formula in case ratio is an "easy division"?

October 9th, 2018, 08:21 AM  #9 
Global Moderator Joined: Dec 2006 Posts: 20,933 Thanks: 2207 
I didn't suggest memorizing it. I used it because I realized it would be easier.

October 9th, 2018, 08:29 AM  #10 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038 
Not important...just fooling around...


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milk, mixture, percentage, resultant 
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