Sophism #13: The Missing Dollar
Bart's Cookie Store is selling two types of cookies - vanilla and chocolate. Vanilla cookies sell at $1 per three pieces, while chocolate ones sell at $1 per two.
At the beginning of the day Bart had 30 vanilla and 30 chocolate cookies. He sold all of them successfully (to his dad, of course), earning $10 + $15 = $25.
Next morning Bart stocked up with 30 vanilla and 30 chocolate cookies again, but decided to simplify his accounting: "Selling 30 cookies at $1 per 2 pieces and another 30 cookies at $1 per 3 pieces is way too complicated. Why don't I bundle things up and sell all 60 cookies at $2 per 5 pieces. Dad buys all of them anyway, so it's easier and result should be the same!"
Having done as decided, Bart sold all his cookies this day as well. Unfortunately, he discovered only $24 dollars in his cash register by the end of the day. Apparently, one has gone missing. Or hasn't it?
For other sophisms check out my other posts.
This one is easy, if you express this in fractions it is evident those two alternatives are not equivalent:
301/3 + 301/2 != 60* 2/5
I don't think expressing the computation in fractions "explains" the problem well enough here. It simply shows that the end results ($25 and $24) are different, which is also stated in the text anyway. The problem is in the (false) intuition that selling "2 per $1 and 3 per $1" must be equivalent to selling "5 per $2" in this particular situation.
(But in general it is not meant to be a complicated puzzle, indeed).