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

Line 7: | Line 7: | ||

==Solution== | ==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> | ||

+ | |||

+ | <math>\frac{x+1}{y+1}=\frac{1.1x}{y}</math> | ||

+ | |||

+ | <math>(x+1)(y)=(1.1x)(y+1)</math> | ||

+ | |||

+ | <math>xy+y=1.1xy+1.1x</math> | ||

+ | |||

+ | <math>y=.1xy+1.1x</math> | ||

+ | |||

+ | <math>10y=xy+11x</math> |

## Revision as of 17:46, 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