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TLDR:
1) Consistent diet with less added sugar.
2) Consistent, regular exercise (competitive swimming is great)
I'm of the same general opinion as bHappY: you're better off taking a long-term stance.
I'm guessing you've got an event (a dance?) coming up that you're trying to get ready for (and kudos to you for being aware of it months in advance!), but 10-15 lbs a month is unhealthy for a 13-year old. In my very unprofessional opinion.
Losing weight and being in shape is more of a lifestyle choice than a quick fix. Be consistent in your good diet choices and regular exercise. There's a bunch of science saying sugar is one of the main causes for child obesity, so that's a good place to start cutting back (links below). In terms of exercise, even just 15 minutes a day of intense exercise will help you get more fit (but 60-90 min/day of moderate exercise is better). Just be sure you're consistent and doing it on a regular basis. In my personal experience, 10-15 hours a week of competitive swimming at age 13 got me from 15% to 8% body fat, and was much easier on my joints than running.
All in all, I wish you the best!
A few links on sugar:
articles.mercola.com/.../...ohol-and-fructose.aspx
blogs.scientificamerican.com/.../
articles.mercola.com/.../can-sugar-be-toxic.aspx
(this article is pretty science-heavy, but it covers the chemistry of why "sugar" is bad for you in the amounts to which we're being exposed)
Links on exercise:
www.lifetime-weightloss.com/.../...day-enough.html
www.fitnessblender.com/.../
At your age you are still growing in height. You don't know what your final height will be so you don't know what your final weight should be. At your age you need proper nutrition now more than ever. Just get some decent exercise, and use common sense with your diet. You probably already have a pretty good idea about the kind of foods that are good and not good, so use common sense. Stay away from the obvious garbage foods, excessively fat foods, soft drinks, candy etc. Soft drinks are horrible, and it's a good idea to quit them completely.
A "perfect" diet can be complicated and hard to achieve. But an improvement over your current diet shouldn't be too hard to do. Just don't get in too much of a hurry to lose weight at your age. Give yourself good nutrition, and let your body will find it's own height and weight over time.
I don't think a full on diet would be good at your age hun. Just try things like less fast food, cut out sugar as much as you can and you could try to do athletics at school or maybe walk around your neighborhood with a friend to be more physically active. But you definitely don't need to to lose 20-30 lbs in a couple months. That doesn't sound too healthy for anyone
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Check out my questions page, my friend lost 70lbs in 4 months under my guidance using only nutrition, and no exercise.
use this calculator to determine how many calories you'll need to take in everyday in order to lose weight at a rate that will allow you to reach your goal.
https://www.calculator.net/calorie-calculator.html
The younger you are the easier it is to lose weight.
If you want to lose weight, it's pretty simple and healthy
1st off you want to change your diet, eat healthy foods, reduce your red meat intake, eat more vegetables, drink water, eat salads with homemade dressing, eat more fish
2nd you want to eat 6 small meals a day, instead of eating 3 large ones
3rd a little exercise for your diet will help, try swimming or light jogging, nothing too serious
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