Respuesta :
let's firstly convert the mixed fractions to improper fractions and then proceed.
[tex]\stackrel{mixed}{4\frac{2}{3}}\implies \cfrac{4\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{14}{3}}~\hfill \stackrel{mixed}{1\frac{1}{4}}\implies \cfrac{1\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{5}{4}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{array}{ccll} batches&cups\\ \cline{1-2} 1&\frac{14}{3}\\[1em] \frac{5}{4}&x \end{array}\implies \cfrac{1}{~~ \frac{5}{4}~~}=\cfrac{~~ \frac{14}{3}~~}{x}\implies \cfrac{\frac{1}{1}}{~~ \frac{5}{4}~~}=\cfrac{~~ \frac{14}{3}~~}{\frac{x}{1}}\implies \cfrac{1}{1}\cdot \cfrac{4}{5}=\cfrac{14}{3}\cdot \cfrac{1}{x} \\\\\\ \cfrac{4}{5}=\cfrac{14}{3x}\implies 12x=70\implies x=\cfrac{70}{12}\implies x=\cfrac{35}{6}\implies x=5\frac{5}{6}[/tex]
