You cannot calculate weights to percentages. Percentages are comparisons of two related quantities so you can have one weight as a percentage of another weight, but not by itself.
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Percentages are percentages - simple! The marketing people have not yet come up with "new improved" percentages.
It is 100*staff costs/total costs.
To find x as a percentage of y, calculate 100*x/y.
A weighted average is a more accurate measurement of scores or investments that are of relative importance to each other. Identify the numbers to be used, identify the weights of each number, convert percentages to decimals, multiply each number by its weight, and add them together to get the weighted score.
To calculate X, as a percentage of Y, divide (100*X) by Y.