Question

A restaurant customer left $1.05 as a tip. The tax was 8% and the tip was 15% of the cost including tax.

What was the total bill?

Answer 1

well, the total bill doesn't include the tip, so the total bill is the cost plus the tax.

so assuming the total bill means before tax, let's call it "x", now if we apply the tax to "x", hmmm how much is 8% of "x"?

`\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{8\% of x}}{\left( \cfrac{8}{100} \right)x}\implies 0.08x`

so "x" plus the tax will just be x + 0.08x = 1.08x.

The tip was 15% of that 1.08x, and we happen to know that was $1.05.

`\begin{array}{ccll} Amount&\%\\ \cline{1-2} 1.08x & 100\\ 1.05& 15 \end{array} \implies \cfrac{1.08x}{1.05}~~=~~\cfrac{100}{15} \\\\\\ 16.2x=105\implies x=\cfrac{105}{16.2}\implies x\approx 6.48`