Question

The number of feet between 2 objects varies directly as the number of miles. If the distance between 2 objects is 2 1/2 miles or 13,200 feet how many feet are equivalent to a distance of 7 miles

Answer 1

`\bf \qquad \qquad \textit{direct proportional variation}\\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ -------------------------------`


`\bf \stackrel{feet}{f}=k\stackrel{miles}{m}\textit{ we also know that } \begin{cases} m=2(1)/(2)\\ f=13200 \end{cases}\implies 13200=k\cdot 2(1)/(2) \\\\\\ 13200=k\cfrac{5}{2}\implies \cfrac{13200\cdot 2}{5}=k\implies 5280=k \\\\\\ \boxed{f=5280m} \\\\\\ \textit{when m = 7, what is \underline{f}?}\qquad \qquad f=5208(7)`