Question

1) A gallon jug of milk is 3/4 full. After breakfast the jug is 1/12 full. How much milk did your family have at breakfast?

Answer 1

well, your family really ate "x" for breakfast, was pretty good with cereal and strawberries btw.

let's keep in mind that the LCD of the denominators 4 and 12 is "12", so we'll use that to do away with the denominators.

`\stackrel{\textit{before breakfast}}{\cfrac{3}{4}}~~ - ~~\stackrel{for~breakfast}{x}~~ = ~~\stackrel{leftover}{\cfrac{1}{12}} \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{12}}{12\left( \cfrac{3}{4}-x \right)~~ = ~~12\left( \cfrac{1}{12} \right)}\implies 9-12x=1 \\\\\\ 9=12x+1\implies 8=12x\implies \cfrac{8}{12}=x\implies {\Large \begin{array}{llll} \cfrac{2}{3}=x \end{array}}`