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.