If w whistles cost c cents, how many whistles can you get for d dollars?
d$ = 100d¢
You want to convert dollars to whistles:
100d¢ * (w whistles)/c¢ = 100dw/c whistles
The easiest way to do this kind of thing is to treat it as a conversion from one unit to another. You can always multiply by 1 without changing anything. Since
w whistles = c cents,
(w whistles)/(c cents) = 1
You enter such conversion factors to make the units you don't want cancel out.