2017 AMC 10B Problem 5

There are fewer cherry jelly beans, so give that number a name and write everything else in terms of it.

1. Let $c$ be the number of cherry jelly beans at the start. Blueberry is twice as many: $2c$.
2. After eating $10$ of each, she has $c - 10$ cherry and $2c - 10$ blueberry.
3. Now blueberry is three times cherry:
$$2c - 10 = 3(c - 10) = 3c - 30.$$
4. Add $30$ to both sides and subtract $2c$: $c = 20$.
5. The question asks for blueberry at the start: $2c = 40$.
6. Check: at the start $40$ and $20$ (twice as many). After eating, $30$ and $10$ (three times as many).

The answer is $\boxed{\textbf{(D)}\ 40}$.

Two "times as many" facts about the same two amounts, one before and one after a change, give one equation with one unknown. Name the smaller amount, write the larger one using the first fact, then use the second fact on the changed amounts. Before answering, re-read which amount the question wants.

Test the choices as the blueberry count. With $40$ blueberry there were $20$ cherry; after eating $10$ of each there are $30$ and $10$, exactly three times. Checking the others: $50$ blueberry and $25$ cherry leaves $40$ and $15$, not three times; the smaller choices fail the same way.