In a bin at the Coolio Convenience Store, there are 200 candies. Of these candies, 90% are black and the rest are gold. After Yasmine eats some of the black candies, 80% of the remaining candies in the bin are black. How many black candies did Yasmine eat?
The number of black candies are:
9/10 * 200 = 180
The number of gold candies are:
1/10 * 200 = 20
Now we let x represent the number of black candies she ate.
180-x is the number of black candies left, 200-x is the total number of candies left. This final fraction is 8/10(because the numerator is black candies and denominator total candies)
\(\frac{180-x}{200-x}=\frac{8}{10}\\ 1800-10x=1600-8x\\ 200=2x\\ x=100 \)
Therefore Yasmine ate \(\boxed{100\ \text{candies.}}\)