Question

5/6 of Java’s pet are cats. She has 90 pets in total. 4/5 of the cats are calico. How many pets are calico pets

Answer 1

well, Java has 90 pets total, 5/6 of those are cats, namely (5/6)*90 are cats.

we also know that 4/5 of her cats are calico, namely

$\bf \stackrel{\frac{5}{6}\textit{ of a total of 90}}{\left( \cfrac{5}{6}\cdot 90 \right)}\implies \cfrac{5\cdot \stackrel{15}{~~\begin{matrix} 90 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}{~~\begin{matrix} 6 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies 75 ~\hfill \stackrel{\frac{4}{5}\textit{ of 75 cats}}{\cfrac{4}{~~\begin{matrix} 5 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\cdot \stackrel{15}{~~\begin{matrix} 75 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}\implies 60$