Jin loves carrots! Yesterday she ate $$\frac{1}{2}$$ of her carrots, and today she ate $$\frac{2}{3}$$ of the remaining carrots. She then discovered that she had $$12$$ carrots left. Yesterday she must have started with  carrots. 
Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Base
If $$12$$ carrots are left after Jin eats $$\frac{2}{3}$$ of today\textquotesingle s carrots, then $$12$$ carrots are $$\frac{1}{3}$$ of the carrots she started with today. So Jin began today with $$36$$ carrots. Since Jin ate $$\frac{1}{2}$$ yesterday, she started with $$2\times36$$ carrots. 