The Beating of our Hearts is the Only Sound (Heart Rate Monitors & Exercise)
Exercise and nutrition is simple. To lose weight, you need to create a caloric deficit = burn more than what you take in. A pound of fat is equivalent to 3,500 calories.
If you don't want to track and log the calories, you need to focus on the exercise side of things and ensure that you burn enough calories, and that you are in the proper range/zone of your heart rate to burn more calories.
Wearing a heart rate monitor will keep you constantly informed of what your heart rate is and if you're within the target heart rate zone. It's simple: work hard enough to be in the target heart rate zone and you will be burning fat. To burn even MORE calories, focus on full-body resistance exercises to recruit more muscle groups and make the body work harder.
If you really want to use your time efficiently, do Circuit Training. Circuit training can replace cardio altogether. Essentially, you eliminate rest periods and just keep moving from one exercise to the next. Studies have shown that circuit training is often more beneficial than doing cardio alone.
Some ideas for recruiting more muscle groups during your circuit training: use a bosu or balance disc/board to add a "controlled instability" element when you're doing curls or squats or presses; do more body-weight resistance exercises;