In a bin at the Cayley Convenience Store, there are 200 candies. Of these candies, $90 \%$ are black and the rest are gold. After Yehudi eats some of the black candies, $80 \%$ of the remaining candies in the bin are black. How many black candies did Yehudi eat?
(A) 2
(B) 20
(C) 40
(D) 100
(E) 160
Solution 1

Of the original 200 candies, since $90 \%$ (or 180 candies) are black, then $10 \%$ (or 20 candies) are gold.

Since Yehudi eats only black candies, the number of gold candies does not change.

After Yehudi has eaten some of the black candies, the 20 gold candies then represent $20 \%$ of the total number of candies, so there must be 100 candies in total remaining.

Thus, Yehudi ate $200-100=100$ black candies.

## Solution 2

Of the original 200 candies, $90 \%$ or 180 candies are black.

Suppose that Yehudi eats $b$ black candies.

This will leave $200-b$ candies in total, of which $180-b$ are black.

Since $80 \%$ of the remaining candies are black, then $\frac{180-b}{200-b}=\frac{4}{5}$ or $5(180-b)=4(200-b)$ or $900-5 b=800-4 b$ or $b=100$.

Thus, Yehudi ate 100 black candies.

ANswer: (D)

#