Is this a good, healthy plan to lose weight, get in shape and stay that way?

I'm 18 and about forty pounds overweight. I've tried a lot of diet plans and workout schemes in my life before, and I'd given up for a long time. Now I've started going to the gym with friends five days a week, and I was wondering if this plan will help me lose weight in a healthy way and, if I follow it, help me stay more lean and toned.

Note: I go to the gym at night, can't do running exercises (bad knees) and am very much a beginner!

Monday, Wednesday, Friday:

In the afternoon, do a thirty minute free-weight session in my room for arms, abs and back.

Go to the gym, do 20-30 minutes of cardio on the elliptical or bike, and do weight machines for arms, abs and back.

Tuesday and Thursday:

Do 20-30 minutes of cardio on the bike or elliptical, then do legs and butt exercises on weight machines.

I'm also eating healthier, but I don't want to go on a diet or cut food out because I won't stick to it.

Will this help me lose weight and get in shape?

Thanks in advance for your opinions!

You can do all the exercising you want, but if you consume more calories than what you burn via exercise and just living (it's amazing how many calories you burn by just living) you will not lose any weight. My suggestion, after losing 90lb myself this past year, is to do a combination of both exercise and diet change. Not just a crash diet, but a real lifestyle diet change. One that would be very beneficial to the point that you keep going even after you are done losing weight. The best foods, in my opinion, are any whole foods like fresh fruit and vegetables. If you slowly add these foods into your diet while at the same time reduce the processed foods, you'll be able to lose a lot of weight and should be able to stick with it. I know it's hard to do, but once you get used to it, you'll really enjoy whole foods over the processed stuff.