The weight of $\frac{1}{2}$ of a whole watermelon together with $4\frac{1}{2}$ cups of chopped grapes is the same weight as $\frac{4}{5}$ of a whole watermelon together with $1\frac{1}{4}$ cups of chopped grapes. A cup of chopped grapes weighs $\frac{1}{5}$ of a pound. What is the weight, in pounds, of a whole watermelon?