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2007A Christmas Shopping Riddle
William went Christmas shopping. He spent half of his money on his sister's Christmas present, and a third of his money on his brother's Christmas present.
After that, he spent two-thirds of the remaining money on his mother's Christmas present, and then he had twenty dollars left, which he gave to his father.
How much money did William start out with? Please explain your answer!
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A Christmas Shopping Riddle Solution
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]
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