When I'm writing math problems for competitions, I work hard to avoid anything that might be considered "ambiguous." However, since the Brainfood pages focus more on language than mathematics, I thought it would be appropriate to introduce an element that might be construed as ambiguous, but really wasn't. I'm referring to the phrase "and a third of his money," which a few people interpreted as "a third of his remaining money." But that's not what was said, and since, in the second paragraph, I use the phrase "remaining money," it should be clear that there really is no ambiguity.

A few people got tripped up by this.

Here's the solution: At the end, William had twenty dollars, which means he spent forty dollars on his mother (because 40 is 2/3 of 60, and 20 is 1/3 of 60).

William spent 1/2 + 1/3 = 5/6 of his money on his brother and sister, so 1/6 of his money must have been $60. Thus, he began with $360.

There is, by the way, a silly story that goes with this problem: [url=http://www.fifteenminutesoffiction.com/gallery.asp?gid=70]William Goes Shopping[/url]