Problem Solving

Whats the easiest way to figure out problems that involve miles, kilometers, inches, ft, and such like when the problem says

There are 5,280 feet in 1 mile and 12 inches in one foot. How many inches are in a mile? I'm given plently of information. I think hey I'll set up a ratio and end up with the wrong answer what gives.
5280ft = 1mile
12in. = 1ft

I am just confused as to why you are setting up a ratio here.

5280 feet in a mile = 5280(1ft) = 1mile

12 in in a foot = 1ft = 12in

So 5280(12in) = 1mile
63360in = 1 mile

This is substituting like you substitute a variable in an algebraic equation.

5280(x) = 1m

x = 12i

5280(12i) = 1m
63360i = 1m

-Carrie