Should you do weight training before cardio?

I read an article online that was saying doing cardio before weight training is counter productive and that you should do weight training before cardio because when you weight train first, you're burning off the carbs, and when you do your cardio you're actually burn off the fat?

I generally do weight training for about 15-20 minutes. I do about 7 or 8 different machines, and I also do 50 minutes on the elliptical daily. By putting weight training first on the days I do both, would that actually help burn fat faster?

Good question.

Cardio is best done as soon as you wake up. This keeps your metabolism up at a high rate for the entire day. Ideally, you should run in the morning and lift in the evening. This will maximize the benefit of the cardio without taxing your energy when it comes time to lift.

BUT...

If you have to fit everything into a single session (i.e. a 1-hour slot before or after work) it is much better to lift before cardio. Otherwise, you will be too fatigued to get a decent weight workout.

Also, it is important to eat enough carbohydrates before a weight workout to promote muscle growth. By doing cardio after you lift, you are giving yourself an opportunity to burn off any excess carbs still left in the tank.

getting your heart rate up BEFORE you weight train helps you to burn fat while you weight train. The only disadvantage is that it may take away from your strength and ability to weight train - which is why some people recommend doing it after weight training. In terms of fat loss, cardio -> weights is better for the short term. Long term - spend more time on weights. Because the more muscle you build the higher your metabolism (fat loss) will be WITHOUT cardio.

You should do a little bit of Cardio before you do the weight training, just to get your body to the right temperature. Depending of the outside weather and how you got to the Gym (Bike, walking ...car...) the cardio before the training is not mandatory.
After the weight training you should do a 15-20 cardio workout.