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Get a stability ball. It can help build your core strength and improve your balance. You can also use it to tone your glutes and legs.
Jump rope for 15 minutes and you'll get a great cardio workout. A jump rope with non-slip foam handles is the best.
Or try hula hooping. Not only is it a good cardio exercise but it's also great for your core!
Elastic bands or tubes are also great items to have. Use them for resistance training to strengthen and tone your muscles.
A pair of free weights costs $10 to $60. If you can, buy two pairs - a lighter pair to work your arms and shoulders and a heavier pair to work your back and chest.
You'll probably want an exercise mat. The extra cushioning is helpful for push-ups and other exercises you do on the floor. A mat is about $20.
Aim for 30 minutes of aerobic exercise five days a week and strength training two to three days a week.