Julia spent 1/3 of her birthday money then she lost half of the rest now she has only $10 left how much did she get for her birthday

She got $30, because 10 is 1/3 of 30. Think of it like this. What's 10·3? If it was 1/6, she would have 60 dollars, because 10 ·6 is 60. The equation here, if your teacher is asking for that, would be (x/3=10), or (10·1/3=x). X represents the variable.