Question

a furniture store is having a weekend sale and is offering a 20% discount on patio chairs and tables. the sales tax on furniture is 6.25%. using function composition how can you represent the total amount, A, that you would need to pay for furniture that costs X dollars?

Answer 1

well, we know the store is having a 20% off sale, so if you go and buy a few items and the total cost is X, well, since the items are on sale, you won't be paying 100% of X, you'll be paying only 100% - 20% = 80% of X, hmmm how much is 80% of X anyway?

`\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 0.80X \\\\[-0.35em] ~\dotfill\\\\ ~\hspace{12em}\stackrel{ \textit{total amount} }{A}~~ = ~~0.80X`