Mixtures and allegations , Weighted averages ,scale methods or by any other name.
As is our wont , this post too is bottoms up i.e we start with the simplest idea and build along adding various factors of difficulty as we progress. And the need to drive home the process of basics first approach. Your understanding and our effectiveness has to be based upon a common vocabulary or as Voltaire put “terms definition” . Therefore it is paramount that you proceed linearly across this post , especially if mathematics normally leaves you hassled . Those proficient at it may start from the last problem and work backwards .
The beauty of training videos ( not specifically these ) that one tool at the same time can cater to different levels of learning speed. A slow learner can pause and notice each step as it unveils in accordance with the question statement . an for a fast learner 20 minutes flat expose him to the depth of the subject.
We recommend starting with the pre-reading slide show since the video some times may leave you panting and lost , so make sure we are talking in the same language before you start with the videos.
Pre reading for Weighted Averages
in the slide show , the basic formula , an example to come to the formula , scale method , basic examples , understanding rates and weights
Click on the image to launch the lesson.
weighted averages using Scales in action
presence of multiple ratios
is confusing for most people. the task though is quite easy if you think with the right questions in mind and approach the question actively much like the key to effective reading. So the questions should be ” whatever ratio/percent I am seeing , what two things does it represent ? . Start with this question and apply it to any ratio or percent relation you see and the data should unravel itself.
As the questions in following videos get solved notice the placement of ratios in their appropriate place and see if you can establish the connections along with the video. Pause , rewind , loop again to understand better.
Applications in non mixture cases
The challenge is to recognize the rates and the weights and having your ratios and pld basics handy . As the problems unfold , try and identify the rates and corresponding weights.
Hidden ratios
so now you know the scale and you know how to identify various information pieces as rates and weights. yet , some problems will still mangle your thought processes . Chances are in these questions the information is not given in the language and way you are expecting it . This problem can be easily resolved if you translate the problem for your self in terms that you know of .
In the following cases the ratio of W1 and W2 is not given in the usual way (compare to previous problems). The trick is to identify these ratios in the language.
Essentially in the case where the volume of a solution is increased by X % , the ratio of W1 to W2 is 100 to X , so if 20% increases the ratio of W1 and W2 is 100:20 i.e 5:1
in the case where X% is removed and replaced the ratio of W1 and W2 is 100-X : X , so if 20% was removed and replaced the ratio of W1 and W2 is 80:20 i.e 4:1
Comprendez?
yes //no//maybe so ?