AMC 12B 2007 Problem 24

How many pairs of positive integers (a, b) are there such that \operatorname{gcd}(a, b)=1 and

\dfrac{a}{b}+\dfrac{14 b}{9 a}

is an integer?

Answer Choices
A. 4
B. 6
C. 9
D. 12
E. infinitely many