Question

A bag with 2 1/6 ounces of peanuts can make 2/5 of a jar of peanut butter. It can make a full jar with how many ounces of peanuts?

Answer 1

$\bf \begin{array}{ccllll} \begin{array}{llll} peanut\\bat \end{array}& \begin{array}{llll} peanut\\jar \end{array}\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 2\frac{1}{6}&\frac{2}{5}\\\\ x&1 \end{array}\implies \cfrac{2\frac{1}{6}}{x}=\cfrac{\frac{2}{5}}{1}\implies \cfrac{\frac{2\cdot 6+1}{6}}{\frac{x}{1}}=\cfrac{\frac{2}{5}}{\frac{1}{1}}$

$\bf \cfrac{\frac{13}{6}}{\frac{x}{1}}=\cfrac{2}{5}\cdot \cfrac{1}{1}\implies \cfrac{13}{6}\cdot \cfrac{1}{x}=\cfrac{2}{5}\implies \cfrac{13}{6x}=\cfrac{2}{5}\implies 13\cdot 5=2\cdot 6x \\\\\\ 65=12x\implies \cfrac{65}{12}=x\implies \boxed{5\frac{5}{12}=x} \\\\\\ \cfrac{5\cdot 12+5}{12}\implies \cfrac{65}{12}$