Question

a souvenir of the eiffel tower is scaled 1/80 at inch to 1 foot. if the total height of the tower is 1,069 feet, the approximate height of the souvenir of the eiffel tower to the nearest tenth is

Answer 1

well, let's convert 1 foot to inches, that'd be 12 inches per foot.

so we know that the souvenir is 1/80 in, to the actual of 12 inches on the Eiffel Tower, if the Tower itself is 1069 feet high, namely (1069)(12) inches, how high is the souvenir?

`\begin{array}{ccll} \stackrel{in}{souvenir}&\stackrel{in}{actual}\\ \cline{1-2} (1)/(80)&12\\[1em] x&(1069)(12) \end{array}\implies \cfrac{ ~~ (1)/(80) ~~ }{x}~~ = ~~\cfrac{12}{(1069)(12)}\implies \cfrac{ ~~ (1)/(80) ~~ }{(x)/(1)}~~ = ~~\cfrac{12}{12828} \\\\\\ \cfrac{1}{80}\cdot \cfrac{1}{x}=\cfrac{1}{1069}\implies \cfrac{1}{80x}=\cfrac{1}{1069}\implies 1069=80x\implies \cfrac{1069}{80}=x\implies 13.4\approx x`