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I eat a egg sandwich for breakfast
That's probably your first mistake. Egg yolks are
loaded with fat. In fact, one egg yolk has almost your entire day's fat limit. If there is cheese or sausage on that sandwich, then you're probably over your limit.
So either ditch eggs or just eat the whites. Fruits, vegetables, and whole grains would also be good options.
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I don’t eat lunch because my school tries to make me eat at 10AM which is ridiculous
That's probably your second mistake. If you're trying to lose weight, you should ideally be eating small meals/snacks often. That makes your metabolism say, "I guess I can run fast and burn all the fat I want; no need to store if I'm getting it often enough!" If you go all day without eating, on the other hand, your metabolism says, "I don't know what's going on out there...I better slow down and hang onto some of this fat in case there is a food shortage..."
So eat a small breakfast, then bring a small and healthy snack for lunch.
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Now Why did I gain Half a pound?
Fat does weigh more. So don't worry so much about what the scale says.
So:
-Make sure you are drinking plenty of water.
-Cut down on fat. Be careful with dairy and meat in particular.
-Cut down on sugar. Be careful of soda, cookies, cakes, etc.
-Be careful with pre-packaged foods. They often have a lot of fat, sugar, salt, or all three.
-Be careful with eggs.
-Read nutrition labels. Pay attention to fat content.
-Keep up with the cardio.