Question

it takes someone 15 minutes to prepare 3 1/4 cups of juice how many hours would it take to prepare 32 1/2 cups of juice​

Answer 1

`\bf \begin{array}{ccll} minutes&\stackrel{juice}{cups}\\ \cline{1-2} 15&3(1)/(4)\\\\ x&32(1)/(2) \end{array}\implies \cfrac{15}{x}=\cfrac{3(1)/(4)}{32(1)/(2)}\implies \cfrac{15}{x}=\cfrac{(3\cdot 4+1)/(4)}{(32\cdot 2+1)/(2)}\implies \cfrac{15}{x}=\cfrac{(13)/(4)}{(65)/(2)}`

`\bf \cfrac{15}{x}=\cfrac{~~\begin{matrix} 13 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{\underset{2}{~~\begin{matrix} 4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}\cdot \cfrac{~~\begin{matrix} 2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{\underset{5}{~~\begin{matrix} 65 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}\implies \cfrac{15}{x}=\cfrac{1}{10}\implies 150=x\leftarrow \begin{array}{llll} \textit{150 minutes or}\\\\ \textit{2 hours and a half} \end{array}`