# Difference between revisions of "2015 AMC 10A Problems/Problem 15"

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+ | ==Problem== | ||

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+ | 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>? | ||

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+ | <math>\textbf{(A) }0\qquad\textbf{(B) }1\qquad\textbf{(C) }2\qquad\textbf{(D) }3\qquad\textbf{(E) }\text{infinitely many}</math> | ||

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+ | ==Solution== | ||

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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 18:42, 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