Well organized....
But for weighted average, I feel an alternative approach will be easy
Quote:
Percents and weighted averages
Cereal K is 10% sugar and Cereal B is 2% sugar. What should be the ratio of them to produce a 4% sugar cereal?
Technique: Pick a smart number for one of the quantities and call the other quantity x. For example, picking 100 grams for Cereal K:
100*0.1 + 0.02*x = 0.04(100 + x) 10 + 0.02x = 4 + 0.04x
0.02x = 6 x = 300
So, the ratio is 3 parts of Cereal B to each part of Cereal K, or 1:3
10k+2b=4(k+b) ==>6k=2b ==> k:b = 1:3Quote:
Percent Change and Weighted Averages
The revenue from pen sales was up 5%, but the revenue from pencil sales declined 13%. If the overall revenue was down 1%, what was the ratio of pen and pencil revenues?
105 + 0.87x = 0.99(100 + x) 6 = 0.12x x = 50
So, the ratio is 2:1
105Pen+87Pencil=99(Pen+Pencil) ==> 6Pen = 12Pencil ==> Pen : Pencil = 2:1Let me know your thoughts...
In fact this approach can be applied to any mixture problem : add/replace/remove combinations