The length that a hanging spring stretches varies directly with the weight placed at the end of the spring. If a weight of 15 lb stretches a certain spring 19 in., how far will the spring stretch if the weight is increased to 30 lb? (Leave the variation constant in fraction form. Round off your final answer to the nearest in.)
Let $k$ be the variation constant. We have $19=k\cdot 15$, so $k=\frac{19}{15}$. If the weight is increased to 30 lb, let $y$ be the length the spring stretches. We have $y=\left(\frac{19}{15}\right)30=\boxed{38}$ inches.
