A math problem

By Jason Wojciechowski on March 15, 2006 at 4:14 PM

Somebody managed to get to this blog by using the following search: "juan gave two thirds of his baseball card collection to his best friend marcus. he gave one half of the cards he had left to his brother. finally he gave one half of the cards he had left to his sister. he had 25 cards left. how many cards did juan have originally in his collection?" First, that's pretty amazing. Second, let's figure this out, since I am, after all, a former high-school math teacher.

The easiest way is probably to work backwards. If he's got 25 now, and he gave half to his sister, he must have had 25 x 2 = 50 before he gave to his sister. And if he had 50 before he gave to his brother, he must have had 50 x 2 = 100 before he gave to his brother. And if he had 100 after he gave 2/3 to Marcus, then he must have had 100 x 3/2 = 300/2 = 150 before he gave to Marcus.

So to check: 150 x 2/3 = 300 / 3 = 100 x 1/2 = 50 x 1/2 = 25, as he's supposed to have. So he had 150 when he started.

EDIT: I'm stupid. If Juan gave 2/3 of his collection to Marcus, then he retained 1/3. Thus if he had 100 after giving 2/3 to Marcus, he actually had 100 x 3 = 300 before giving to Marcus. Thus the correct answer is 300, and I'm an idiot. Thanks to the rather charitable commenter who pointed this mistake out.

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