Question

when I make macaroni and cheese for my brother and me, I use 2 2/3 tablespoons of butter. how much butter will I n need to make my macaroni and cheese dish for Thanksgiving dinner if 15 people are attending?

Answer 1

if you use 2 2/3 tablespoons for you and your brother, that means, you need 2 2/3 tablespoons for two servings, how many tablespoons for 15 servings then?

well
`\bf 2(2)/(3)\implies \cfrac{2\cdot 3+2}{3}\implies \cfrac{8}{3}\\\\ -------------------------------\\\\ \begin{array}{ccllll} \textit{butter spoons}&servings\\ -----&-----\\ (8)/(3)&2\\ x&15 \end{array}\implies \cfrac{(8)/(3)}{x}=\cfrac{2}{15}\implies \cfrac{(8)/(3)}{(x)/(1)}=\cfrac{2}{15} \\\\\\ \cfrac{8}{3}\cdot \cfrac{1}{x}=\cfrac{2}{15}\implies \cfrac{8}{3x}=\cfrac{2}{15}\implies 8\cdot 15=3x\cdot 2\implies 120=6x \\\\\\ \cfrac{120}{6}=x\implies 20=x`