Question

The Jayden family eats at a restaurant that is having a 15% discount promotion. Their meal costs $78.24 before the discount, and they leave a 20% tip. If the tip applies to the cost of the meal before the discount, what is the total cost of the meal? Round your intermediate calculations and answer to the nearest cent. The total cost of the meal is $

Answer 1

so the meal is 78.24 and the tip applies to that amount, now we're assuming "the total cost" means the "price of the meal" plus the tip, so let's first check what the tip is, hmmm 20% of 78.24, if we take 78.24 to be the 100%, what is 20% off of it?

$\begin{array}{ccll} amount&\%\\ \cline{1-2} 78.24&100\\ x&20 \end{array}\implies \cfrac{78.24}{x}=\cfrac{100}{20}\implies \cfrac{78.24}{x}=5 \\\\\\ 78.24=5x\implies \cfrac{78.24}{5}=x\implies 15.648=x$

we know the meal is going the be discounted by 15% anyway, so if 78.24 is the 100%, how much is 15% off of it in percentage?

$\begin{array}{ccll} amount&\%\\ \cline{1-2} 78.24&100\\ x&15 \end{array}\implies \cfrac{78.24}{x}=\cfrac{100}{15}\implies \cfrac{78.24}{x}=\cfrac{20}{3} \\\\\\ 234.72=20x\implies \cfrac{234.72}{20}=x\implies 11.736=x$

$\stackrel{\textit{\large total cost of the meal}}{\stackrel{\textit{original price}}{78.24}-\stackrel{discount}{11.736}+\stackrel{tip}{15.648}}\implies \underset{\textit{rounded up}}{82.15}$