Question

2/3 cup of juice for every 1/3 cup of oj. How many cups of juice is used for 1 cup of OJ

Answer 1

`\begin{array}{ccll} Juice&OJ\\ \cline{1-2} (2)/(3)&(1)/(3)\\[1em] x&1 \end{array}\implies \cfrac{~~ (2)/(3)~~}{x}=\cfrac{~~(1)/(3) ~~}{1}\implies \cfrac{~~ (2)/(3)~~}{x}=\cfrac{1}{3}\implies \cfrac{~~ (2)/(3)~~}{(x)/(1)}=\cfrac{1}{3} \\\\\\ \cfrac{2}{3x}=\cfrac{1}{3}\implies 6=3x\implies \cfrac{6}{3}=x\implies 2=x`