FDP: Chapter 7- Weighted Averages

[NMencia09]

Hello,

This is from FDP Ch. 7 page 104 #12 vs. #14.

For 12, I used a method taught in one of the Thursday with Ron:
Weighted Average is 50%.
Brand A is 40% (which is 10% less than 50)
Brand B is 65% (which is 15% greater than 15)
So find the LCM--->30. 3 parts of A to 2 parts of B balances out to make the weighted average = 50%. This method seems a lot quicker than setting up tables and solving with equations. It's the unknown multiplier method.

Answer came to 60% of brand A, 40% brand B (3:2 ratio of A:B).

I tried to apply this same method to question 14, which seemed identical to me. This time the weighted average was 8%, with 10% and 5% as the two 'mixes'. Following the same logic I arrived at, again, 60% and 40%, with 60 favoring the 10% portion, and 40 favoring the 5% portion.

The answer, however, came out to slightly above 60%, (61.1%).

I think this has to do with the increase of 10% and 5%, but can someone explain the math behind this? When does first method work vs having to do the full algebra?

Thank you.

[LazyNK]

Hey Noah,
I try to explain to you - I hope you are able to get the concept. The method of calculation you have used for both problems should always work. So, it is not that the simple method without complicated algebric equations doesn't work for question 14 - it works just as well as it does for question 12.
Here is the maths behind this:

For problem 12, the question is what is the ratio of two different mixtures in the overall mixture(mixture of the two mixtures). The solution obtained is A/B=3/2, exactly as you solve.

For problem 14 however, if the question were, what is the ratio of original no. of revolutionary voters to original no. of status quo voters, say R/S . Then your answer R/S=3/2 would be correct. But here the question is, what is the ratio of new no. of revolutionary voters to new no. of status quo voters i.e. a particular mix of R(Revolutionary voters) and S(Status Quo voters) was present, and later, R increased by 10% and S by 5%, so a new ratio of revolutionary/status quo results, say R_new/S_new. How to calculate this w/o the complex algebra ? Since we are told that the revolutionary increased by 10% and status quo increased by 5%, we know that R_new=R*1.1 and S_new=S*1.05 -> R_new/S_new=R*1.1/S*1.05=3/2*22/21=11/7. So, the result 61.1% (=11/18*100).

So, for problems about an existing mixture and a subsequent change in the two components of the mixture, it is important to see whether the question is on the original ratio in the mixture OR on the new ratio.
-NK

[NMencia09]

Excellent explanation, sir! Many thanks.

[tim]

cool; let us know if you have any further questions..

[levinewriting]

Can I post a mixtures question that is not from a manhattan or official source. I need help on the mixtures that you need to remove a portion and add 100% of another portion, seems like these cannot be solved with the scale method.

Thanks

[RonPurewal]

Can I post a mixtures question that is not from a manhattan or official source. I need help on the mixtures that you need to remove a portion and add 100% of another portion, seems like these cannot be solved with the scale method.

Thanks

* Go to the General Math Questions folder.

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Thanks.