|By Azn_Cowboy (Azn_Cowboy) on Sunday, December 29, 2002 - 11:26 am: Edit|
If a/b + (a+10b)/(b+10a) = 2,
what does a/b equal?
|By Quarky on Sunday, December 29, 2002 - 11:59 am: Edit|
LOL. What in the blue hell is AMC? Is it some test for kindergarten kids or what?
One possible OBVIOUS answer is a/b = 1
Of course, if a and b are the same number, then a/b is one, and so is the ratio that is added to it, resulting in a total of 2 (and satisfying the equation).
The other possible answer is 4/5
|By usa on Sunday, December 29, 2002 - 01:34 pm: Edit|
amc = american math competition, also known as the first round exam to get into USA math olympiad, aka a really hard test.
|By Azn_Cowboy (Azn_Cowboy) on Sunday, December 29, 2002 - 02:39 pm: Edit|
Yea, they had to be two distinct integers. Forget to say that.
|By caltech07 on Sunday, December 29, 2002 - 04:54 pm: Edit|
Yeah, this is pretty easy... find the LCD, rewrite the condition as 10a^2 - 18ab + 8b^2 = 0, factor to (10a - 8b)(a - b) = 0, the right is exluded, so we have 10a = 8b, or a/b = 4/5
|By Quarky on Sunday, December 29, 2002 - 11:52 pm: Edit|
Yeah, of course, Idaho is too stupid to administer the AMC, right? BTW, I was just being sarcastic. I knew that AMC was hard. I just didn't know what it was. Thanks for the info, "usa." Where do you guys take this test? What calculators, if any, are you allowed to use?
|By The (The) on Monday, December 30, 2002 - 01:19 am: Edit|
Here's the answer, explained, from the official site:
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