Question

The directions for mixing an insect spray say to use 2 3/4

ounces of chemical in each gallon of water. How many ounces of chemical should be mixed with 4 3/5
gallons of​ water? First, estimate the answer to the application problem. Then find the exact answer.

Answer 1

`\bf \begin{array}{ccllll} chemical(oz)&water(gallon)\\ \textendash\textendash\textendash\textendash\textendash\textendash&\textendash\textendash\textendash\textendash\textendash\textendash\\ 2(3)/(4)&1\\\\ x&4(3)/(5) \end{array}\implies \cfrac{2(3)/(4)}{x}=\cfrac{1}{4(3)/(5)} \\\\ -----------------------------\\\\`


`\bf now\qquad \begin{cases} 2(3)/(4)\implies \cfrac{11}{4}\\\\ 4(3)/(5)\implies \cfrac{23}{5} \end{cases}\qquad and\qquad \cfrac{(a)/(b)}{\frac{c}{{{ d}}}}\implies \cfrac{a}{b}\cdot \cfrac{{{ d}}}{c}\\\\ -----------------------------\\\\ \cfrac{2(3)/(4)}{x}=\cfrac{1}{4(3)/(5)}\implies \cfrac{(11)/(4)}{x}=\cfrac{1}{(23)/(5)}\implies \cfrac{(11)/(4)}{(x)/(1)}=\cfrac{(1)/(1)}{(23)/(5)} \\\\\\`



`\bf \cfrac{11}{4}\cdot \cfrac{1}{x}=\cfrac{1}{1}\cdot \cfrac{5}{23}\implies \cfrac{11}{4x}=\cfrac{5}{23}`

solve for "x"