R4

QUESTION: Tom measures himself to be $182$cm tall and calculates that this new height is a $4\%$ increase on his height 2 years ago. Work out how tall Tom was 2 years ago.

ANSWER: We need to consider how we would calculate a $4\%$ increase. We know that $4\%=0.04$, so we get the multiplier for a $4\%$ increase to be

$1+0.04=1.04$

Let $H$ be Tom’s height from two years ago. We know that the result of multiplying $H$ by $1.04$ must be $182$. We can write this as an equation:

$H\times 1.04=182$

Then, if we divide both sides by $1.04$ we get

$H=182\div 1.04=175$

So, Tom’s height two years ago was $175$cm.