Question

a television normally sells for $499 what is now discounted 25%. The sales tax rate is 6.5%. What is the total cost of television?

Answer 1

hmmm what is now discounted? well, let's assume it sells normally for 499 and is discounted today at 25%, how much is that?

well, if we take 499 to be the 100, how much is 25%?


`\bf \begin{array}{ccll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 499&100\\ d&25 \end{array}\implies \cfrac{499}{d}=\cfrac{100}{25} \cfrac{499\cdot 25}{100}=d \\\\\\ 124.75=d\qquad \textit{so the new price is }499-124.75\implies 374.25`

now, applying the sales tax to the discounted price.

if we take 374.25 to be the 100%, how much is 6.5%?


`\bf \begin{array}{ccll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 374.25&100\\ t&6.5 \end{array}\implies \cfrac{374.25}{t}=\cfrac{100}{6.5}\implies \cfrac{374.25\cdot 6.5}{100}=t`

so, the total cost will then be 374.25 + t.