2015 AMC 10A Problems/Problem 15: Difference between revisions
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==Problem== | |||
Consider the set of all fractions <math>\frac{x}{y}</math>, where <math>x</math> and <math>y</math> are relatively prime positive integers. How many of these fractions have the property that if both numerator and denominator are increased by <math>1</math>, the value of the fraction is increased by <math>10\%</math>? | |||
<math>\textbf{(A) }0\qquad\textbf{(B) }1\qquad\textbf{(C) }2\qquad\textbf{(D) }3\qquad\textbf{(E) }\text{infinitely many}</math> | |||
==Solution== | |||
You can create the equation <math>\frac{x+1}{y+1}=(1.1)(\frac{x}{y})</math> | You can create the equation <math>\frac{x+1}{y+1}=(1.1)(\frac{x}{y})</math> | ||
Revision as of 17:42, 4 February 2015
Problem
Consider the set of all fractions 
, where 
and 
are relatively prime positive integers. How many of these fractions have the property that if both numerator and denominator are increased by 
, the value of the fraction is increased by 
?
Solution
You can create the equation 
