Question

in 3/4 pound of a spice mix there is 5/6 cup of cinnamon. how much cinnamon dose the spice mix contain per pound

Answer 1

`\bf \begin{array}{ccll} \stackrel{lbs}{spice}&\stackrel{cups}{cinnamon}\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ (3)/(4)&(5)/(6)\\\\ 1&c \end{array}\implies \cfrac{(3)/(4)}{1}=\cfrac{(5)/(6)}{c}\implies \cfrac{(3)/(4)}{(1)/(1)}=\cfrac{(5)/(6)}{(c)/(1)}\implies \cfrac{3}{4}\cdot \cfrac{1}{1}=\cfrac{5}{6}\cdot \cfrac{1}{c} \\\\\\`


`\bf \cfrac{3}{4}=\cfrac{5}{6c}\implies 18c=20\implies c=\cfrac{20}{18}\implies c=\cfrac{10}{9}\implies c=1(1)/(9)`