Difference between revisions of "2023 AIME II Problems/Problem 5"
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| − | + | Let <math>S</math> be the set of all positive rational numbers <math>r</math> such that when the two numbers <math>r</math> and <math>55r</math> are written as fractions in lowest terms, the sum of the numerator and denominator of one fraction is the same as the sum of the numerator and denominator of the other fraction. The sum of all the elements of <math>S</math> can be expressed in the form <math>\frac{p}{q},</math> where <math>p</math> and <math>q</math> are relatively prime positive integers. Find <math>p+q.</math> | |
Revision as of 16:29, 16 February 2023
Let 
be the set of all positive rational numbers 
such that when the two numbers and 
are written as fractions in lowest terms, the sum of the numerator and denominator of one fraction is the same as the sum of the numerator and denominator of the other fraction. The sum of all the elements of can be expressed in the form 
where 
and 
are relatively prime positive integers. Find 
