A high school senior was applying to college and wondered how many applications she needed to send. Her counselor explained that with the excellent grade she received in chemistry she would probably be accepted to one school out of every three to which she applied. [3 applications = 1 acceptance] She immediately realized that for each application she would have to write 3 essays, [1 application = 3 essays] and each essay would require 2 hours work [1 essay = 2 hours]. Of course writing essays is no simple matter. For each hour of serious essay writing, she would need to expend 500 calories [1 hour = 500 calories] which she could derive from her mother's apple pies [1 pie = 1000 calories]. Her mother makes her an apple pie every 3 times she cleans her room. How many times would she have to clean her room in order to gain acceptance to 10 colleges?
Okay, this lengthy problem is my homework. Using dimensional analysis, shouldn't it be:
$$(3 \space times / 1 \space pie) \cdot (1 \space pie / 1000 \space cal) \cdot (500 \space cal / 1 \space hr) \cdot \\ (2 \space hr / 1 \space essay) \cdot (3 \space essays / 1 \space app) \cdot (3 \space app / 1 \space acceptance) \cdot 10 \space acceptances$$
? That gave me 270 times, but the answer states that it is 300 times. Where did I go wrong?