Question

If Logan's family can drive 23 1/8 miles on 1 gallon of gas,how far can they drive on 17 gallons

Answer 1

`\bf \begin{array}{ccll} miles&\stackrel{gas}{gallons}\\ \cline{1-2}\\ 23(1)/(8)&1\\\\ x&17 \end{array}\implies \cfrac{23(1)/(8)}{x}=\cfrac{1}{17}\implies \cfrac{(23\cdot 8+1)/(8)}{x}=\cfrac{1}{17}\implies \cfrac{(185)/(8)}{x}=\cfrac{1}{17} \\\\\\ \cfrac{(185)/(8)}{(x)/(1)}=\cfrac{1}{17}\implies \cfrac{185}{8}\cdot \cfrac{1}{x}=\cfrac{1}{17}\implies \cfrac{185}{8x}=\cfrac{1}{17} \\\\\\ 3145=8x\implies \cfrac{3145}{8}=x\implies 393(1)/(8)=x`