Question

On a map, it is 7 1/ 8 from Arlington to Banks. If the scale of the map is 1 1/ 4 per mile, how far is it between the two towns

Answer 1

`\begin{array}{ccll} Map&\stackrel{ miles }{Actual}\\ \cline{1-2} 1(1)/(4)&1\\[1em] 7(1)/(8)&x \end{array}\implies \cfrac{ ~~ 1(1)/(4) ~~ }{7(1)/(8)}~~ = ~~\cfrac{1}{x}\implies \cfrac{ ~~ (5)/(4) ~~ }{(57)/(8)}~~ = ~~\cfrac{1}{x}\implies \cfrac{5}{4}\cdot \cfrac{8}{57}=\cfrac{1}{x} \\\\\\ \cfrac{5}{57}\cdot \cfrac{8}{4}=\cfrac{1}{x}\implies \cfrac{5}{57}\cdot 2=\cfrac{1}{x}\implies \cfrac{10}{57}=\cfrac{1}{x} \\\\\\ 10x=57\implies x=\cfrac{57}{10}\implies x=5.7~miles`

Answer 2

`7 (1)/(8) / 1 (1)/(4) = (57)/(8) / (5)/(4) =`

`(57)/(8) * (4)/(5) = (57)/(10) = 5.7 \: miles`