In 1960, there were 450,000 cases of measles reported in the U.S. In 1996, there were 500 cases reported. How many cases of measles would have been reported in 1987 if the number of cases reported from 1960 to 1996 decreased linearly?
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.
112875
Level 5
Algebra
Problem: In 1960, there were 450,000 cases of measles reported in the U.S. In 1996, there were 500 cases reported. How many cases of measles would have been reported in 1987 if the number of cases reported from 1960 to 1996 decreased linearly?
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To determine the number of measles cases reported in 1987, we first need to establish the linear relationship between the years and the number of cases. The data points we have are from 1960 with 450,000 cases and 1996 with 500 cases. 

We can calculate the slope of the line representing the decrease in cases. The time span from 1960 to 1996 is 36 years, and the change in the number of cases is 450,000 - 500 = 449,500 cases. 

The slope (m) of the line can be calculated as:
m = (change in cases) / (change in years) = -449500 / 36 = -12486.11 (approximately).

This slope indicates that, on average, the number of measles cases decreased by about 12,486 cases per year.

Next, we need to find the year 1987 in relation to our starting point of 1960. The year 1987 is 27 years after 1960 (1987 - 1960 = 27).

Now, we can calculate the number of cases in 1987 by applying the slope to the number of years since 1960:
Cases in 1987 = Cases in 1960 + (slope * number of years since 1960)
Cases in 1987 = 450,000 + (-12486.11 * 27).

Calculating this gives:
Cases in 1987 = 450,000 - 337125 = 112875.

Thus, the number of measles cases reported in 1987, assuming a linear decrease, is 112875.<|END_OF_LATENT|> The final answer is $112875$.