Percentage Change - Link Up

Percentages can be merged with a range of other topics. This worksheet has 22 questions that do just that, and there's fully worked solutions.

As a taster, here are two additional questions.

Solution

Let \(p\) be the number of purple sections, \(g\) be the number of green sections and \(n\) be the total number of sections. Now, \(P(orange\:or\:purple)=\frac{2+p}{n}\) and \(P(orange\:or\:green)=\frac{2+g}{n}\).

Use the percentage to form the equation \[\frac{2+p}{n}=1.05\left(\frac{2+g}{n}\right)\]\[2+p=1.05(2+g)\]\[20p=2+21g\]At this point, we can see that the LHS is a multiple of 20, so the RHS must be too. This means that \(21g\) must end in 8. Trial \(g=8\) and we get \(20p=170\) which is not an integer value for \(p\). Trialling \(g=18\) gives \(p=19\). So the minimum total number of sections is \(18+19+2=39\)

 

Solution

Let the radius be \(r\) then the area is \(\pi r^2\) and the circumference is \(2\pi r\). Set up an equation using the percentage.\[\pi r^2=1.92(2\pi r)\]\[r=3.84\]The diameter is therefore 7.68.