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

(Created page with "You can create the equation <math>\frac{x+1}{y+1}=(1.1)(\frac{x}{y})</math>")
 
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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 $\frac{x}{y}$, where $x$ and $y$ are relatively prime positive integers. How many of these fractions have the property that if both numerator and denominator are increased by $1$, the value of the fraction is increased by $10\%$?

$\textbf{(A) }0\qquad\textbf{(B) }1\qquad\textbf{(C) }2\qquad\textbf{(D) }3\qquad\textbf{(E) }\text{infinitely many}$

Solution

You can create the equation $\frac{x+1}{y+1}=(1.1)(\frac{x}{y})$

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