Question

A small pool can hold 53.5 gallons of

water. It is currently 3/4 full. How many
gallons are in the pool?

Answer 1

keeping in mind that a full pool means a WHOLE or namely 5/5 or 6/6 or for this case 4/4 is a whole, so

`\begin{array}{ccll} gallons&quarters\\ \cline{1-2} 53.5&(4)/(4)\\[1em] x&(3)/(4) \end{array}\implies \cfrac{53.5}{x}~~ = ~~\cfrac{ ~~ (4)/(4)~~ }{(3)/(4)}\implies \cfrac{53.5}{x}~~ = ~~\cfrac{1}{ ~~ (3)/(4)~~ } \\\\\\ \cfrac{53.5}{x}=\cfrac{4}{3}\implies 53.5(3)=4x\implies \cfrac{53.5(3)}{4}=x\implies 40.1 \approx x`