Question

Paula works at an appliance store where they make most of their money on commission. She makes 4.25% commission on the price of any appliance she sells. The store was offering 20% off on washers and dryers. Her first customer bought a washer for $685.96 and a dryer for $475.70 before applying the discount. How much money did she lose because of the sale? Round your answer to the nearest cent.

Answer 1

well, let's take a looksie at what it would have been had there not been a sale, so at regular price the washer and dryer are just 685.96 + 475.70 = 1161.66, well hell how much is 4.25% of that?

`\begin{array}ll \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{4.25\% of 1161.66}}{\left( \cfrac{4.25}{100} \right)1161.66} ~~ \approx ~~ 49.37`

now, since we know the appliances are going to be 20%, that means the appliaces sale price will be 100% - 20% = 80%, so 80% of the original price, well, we know the original price for those two is 1161.66, what's 80% of that?

`\stackrel{\textit{80\% of 1161.66}}{\left( \cfrac{80}{100} \right)1161.66} ~~ \approx ~~ \stackrel{ sale~price }{929.33} \hspace{5em} \stackrel{\textit{4.25\% of 929.33}}{\left( \cfrac{4.25}{100} \right)929.33} ~~ \stackrel{ \textit{Paula's commission} }{\approx ~~39.5}`

well, Paula could have made 49.37, but she ended up with 39.5, 49.37 - 39.5 ≈ 9.87.