Question

a chef uses 4 3/4 cups of broth for 10 servings of soup.how much broth is is one serving . let x represent amount. 4 3/4/10 =x/1

Answer 1

Let's firstly convert the mixed fraction to "improper" and then proceed,

$\bf \begin{array}{ccll} \stackrel{broth}{cups}&servings\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 4\frac{3}{4}&10\\\\ x&1 \end{array}\implies \cfrac{\quad \stackrel{mixed}{4\frac{3}{4}}\quad }{x}=\cfrac{10}{1}\implies \cfrac{\quad \frac{4\cdot 4+3}{4}\quad }{x}=\cfrac{10}{1}$

$\bf \cfrac{\quad \stackrel{improper}{\frac{19}{4}}\quad }{x}=\cfrac{10}{1}\implies \cfrac{\quad \frac{19}{4}\quad }{\frac{x}{1}}=\cfrac{10}{1}\implies \cfrac{19}{4}\cdot \cfrac{1}{x}=\cfrac{10}{1}\implies \cfrac{19}{4x}=\cfrac{10}{1} \\\\\\ 19=40x\implies \cfrac{19}{40}=x$