To Paul Alan:
If it's in your area go round and suss it out. I don't think you have enough info to make a decision yet.
You'll soon pick up if she is a genuine customer feeling ripped off or a moaning cheapskate. Sometimes they use price as an excuse after they've had a falling out or even been dumped! On the other hand she could be sweetness and light and the other fella is charging over the top.
If she tells you the price and it's similar to what you'd charge (and that is the ONLY issue) you could even say "look it's about what I'd charge, I'd stick with the other guy." That demonstrates you are an honest chap, don't undercut and that you aren't desperate.
If she is genuine she'll appreciate your frankness and may tell you more or just hop on board. Or not. If it's right among other work of yours then I'd be tempted to take it on after setting out your stall. (Like telling her you don't ring/text first, don't take doorstep cancellations, do work in the rain or whatever else applies)