jmc

Over the course of $1996-1960=36$ years, the number of cases of measles decreased by $450,000-500=449,500$. So, over the course of $1987-1960=27$, the number of cases would decrease by $\frac{27}{36}\cdot (449,500)=337,125$ cases. Therefore, the number of cases in 1987 would be $450,000-337,125=\boxed{112,875}$ if the number of cases decreased linearly.