If $90$ points equal $40%$, what'd be $85$ and so on?

Question

A full mark for a test is $90$ points (instead of the usual $100$), and the test is $40%$ of a subject. If students get $90$ points, obviously they get full $40%$ for the test. Then, how do we work out if, for example, a student gets $85$ and so on?

Answer 1

Use cross-multiplication (also called the rule of three)

$\dfrac{90\text{p}}{40\%}=\dfrac{85\text{p}}{?}\Rightarrow ?=\dfrac{85*40}{90}=37.7778\%$

Answer 2

Use the rule of three for this:

$$\frac{a}{b}=\frac{c}{x}$$ $$x=\frac{bc}{a}$$ Applying this formula for your question would be something like:

$$\frac{90 score}{40\%}=\frac{85score}{x}$$ then $$x=\frac{40\%85score}{90score}$$ $$x=37.78\%$$

Answer 3

Express $85$ as a proportion of the total and multiply by its 'weighting': $\frac{85}{90}*40 = 37.78$ In answer to tpb261: 90 = 0.4x implies x = 90/0.4 = 225.