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
