Will this diet be effective?

I'm drastically cutting down on carbs but I really am having trouble doing the, say, induction phase of atkins with 20 or less per day. When I take money and time into account I can't eliminate certain things entirely. If I were to limit myself at 30 or 40 carbs per day, however, most of which are, of course, coming from vegetables or meats or maybe some fruits, would this still be an effective way to lose some weight? I've got about 10 pounds I really wanna drop. Thanks!