Question

A jacket is reduced in a sale by 20%. A customer has a

loyalty card for a further 10% off the price.
What is the total percentage reduction in the price of the jacket

Answer 1

x = original price for the jacket

now, let's reduce it by 20%, so hmmm that means the new price is really 100% - 20% = 80% of the original price, how much is that?

`\begin{array} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{80\% of x}}{\left( \cfrac{80}{100} \right)x}\implies 0.8x`

now, from that new price, let's reduce it by 10%, that means the newer price will be 100% - 10% = 90% of this new price of 0.8x, so

`\stackrel{\textit{90\% of 0.8x}}{\left( \cfrac{90}{100} \right)0.8x}\implies 0.72x\hspace{5em}\stackrel{\textit{72\% of the orignal price}}{\textit{a reduction of 28\%}}`