One way to approach this problem is to use a proportion:
(markeds in sample) / (total in sample) = (markeds in population) / (total population)
We can plug in the numbers we know:
15 / 250 = 75 / x
where x is the total elk population. We can cross-multiply and solve for x:
15x = 75 * 250
x = 18,750
Therefore, the best estimate for the elk population is 18,750.