It is not a 3 speed. From my reading of the o.p. she has a Raleigh Caprice (3 sp) and has recently bought an (unamed) steel framed 7 sp with a 48T chainring. Is that about right Pandora? I agree with an earlier poster 14-28 was an extremely common rear set and once upon a time that bike probably had a 52/42 double up front. I don't wish to malign total strangers on the Internet but I would ask the o.p. to make very sure that there are actually 7 speeds and not six. 7 speeds were very rare for that time and with 27" wheels.

If a single speed is so hard to find why not get a cheap double instead? I don't ride up mountains either but I use every usable gear on my triple setup. Every one. Which amounts to around 10 or 12 actual ratios. No one can use all the combinations of two (or three) front rings and seven (or six) rear ones.