What is the quickest way to lose 15 pounds?

That doesn't sound entirely safe (or more importantly healthy). Its reccomended that no more than 1-2 pounds are lost per week, so seven times that seems unfeasible and dangerous. One pound is equal to 3500 calories. So by burning calories you shed some pounds. Your body also needs calorie intake to function, which is recommended at 2500 for men, and 2000 for women (depending on your source). To reduce your calorie intake is suggested by a maximum of 1000 calories. So your body will still have something to run on. If it is too much less than this then your body goes into starvation mode clinging to every calorie its got, so you won't lose anything.

I find time and budget as an issue, so walking is my thing. Weighing 225 pounds means you can burn about 500 to 600 calories by just walking around for 2 hours...that can be going for a stroll through the park or going for some retail therapy. Now, if you were to do that once a day for a week, you'd only just burn through that 3500 calories for that one pound in that week. Assuming you've been eating relatively healthily that is.

If you were to go for more rigorous exercise and step up to the losing 2 pounds a week (or potentially a bit more...even though its ill advised), you'd still be looking at 7 weeks. I would advise setting a realistic (but challenging) goal of losing that 15 pounds in 2-3 months through healthy eating and good old fashioned exercise.