Question

How can you use the concept to figure out if the competition is the correct

Answer 1

well, we can see it this way, hmmm ok, so the recipe is 2 scoops for 1/2 gallon for one pitcher, now we want to make four pitchers, that means 2+2+2+2 scoops, so 8 scoops, how much water?

`\begin{array}{ccll} \stackrel{ mix }{scoops}&\stackrel{water}{gallons}\\ \cline{1-2} 2&(1)/(2)\\[1em] 8&x \end{array}\implies \cfrac{2}{8}~~ = ~~\cfrac{~~ ( 1 )/(2 ) ~~}{x}\implies \cfrac{2}{8}~~ = ~~\cfrac{~~ ( 1 )/(2 ) ~~}{(x)/(1)}\implies \cfrac{2}{8}=\cfrac{1}{2}\cdot \cfrac{1}{x} \\\\\\ \cfrac{2}{8}=\cfrac{1}{2x}\implies \cfrac{1}{4}=\cfrac{1}{2x}\implies 2x=4\implies x=\cfrac{4}{2}\implies x=2 ~~ \checkmark`

yeap, the student is correct.