Actually, I have to apologize, the convertible laptops I provided links to are really not applicable to your needs. Previous to answering your question I was providing answers / recommendations in several different threads where people were looking for convertible laptop / tablets that obviously has a much higher price point.
I guess Carbonate was kinda right call 'em overpriced garbage... at least in your case...
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Unfortunately, the addition of a touchscreen is typically adds a $75 - $100 premium in a laptop so searching for one within a reasonable range of your desired budget may be difficult and will take more time....
14" Lenovo Z410 = $500 with Core i3-4000m / 4.4lbs starting weight
http://shop.lenovo.com/us/en/laptops/ideapad/z-series/z410/
14" Lenovo IdeaPad U430p = $549 / $559 depending on the color. Similar to the Z410, but this is an ultrabook so you get a lighter laptop that is easier to carry around. 3.8lbs starting weight
http://shop.lenovo.com/us/en/laptops/ideapad/u-series/u430p/
14" Lenovo Flex = $549 with the Core i3-4010u. Do not get the much weaker Celeron version for $449. You will likely regret your decision sooner rather than later if you buy the cheapest one. TOUCHSCREEN. It is similar to the Yoga, but you cannot fold the screen all the way back to turn it into a tablet. 4.4bls.
http://shop.lenovo.com/us/en/laptops/ideapad/flex/flex-14/
15.6" ThinkPad E545 - Business laptop with an AMD APU so you can also play games. Base price $439 with a relatively weak dual core A6-5350m and a relatively weak graphics core as well. Add the $70 option for the quad core A10-5750m and you can play games with the current most powerful integrated graphics core; the Radeon HD 8650g... oh yeah... you can also do school work too (boooorinnngggggg...zzz, zzz, zzz). Average weight for a 15.6" laptop at 5.4bls.
http://shop.lenovo.com/us/en/laptops/thinkpad/e-series/e545/
That's all for now. I got other things I need to do tonight....