The weight of $\frac{1}{2}$ of a whole roasted chicken together with $4\frac{1}{2}$ cups of green beans is the same weight as $\frac{3}{4}$ of a whole roasted chicken together with $1\frac{1}{2}$ cups of green beans. A cup of green beans weighs $\frac{1}{6}$ of a pound. What is the weight, in pounds, of a whole roasted chicken?