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rbzima
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Homework Statement
The sum of 5 positive real numbers is 100. Prove that there are two numbers among them whose difference is at most 10.
Homework Equations
Nothing really...
The Attempt at a Solution
The biggest problem I'm running into is that I can think of specific examples, but translating that into an algebraic argument has always been my weak area. Getting started is where I struggle the most... but I'm thinking the following:
Let's assume there are no two positive real numbers whose difference is at most 10.
Let [tex]a_{1}, a_{2}, a_{3}, a_{4}, a_{5}[/tex] each represent some positive real number whose sum equal 100. Given that [tex]a_{1}[/tex] is the smallest real number, [tex]a_{2} = 10 + a_{1}[/tex], [tex]a_{3} = 10 + a_{2}[/tex] and so on...
Don't really know where to go from here! Suggestions?
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