Use proportional relationships to solve mixture problem. The incoming 6th-grade class has a choice between band or choir as and elective. There are four times as many seats in choir as there are in band. How many students can choose band if there is a total of 250 students?
Let's say the number of seats in the band is x.
Since there are four times as many seats in the choir as there are in the band, the number of seats in the choir is 4x.
The total number of seats for both band and choir is x + 4x = 5x.
But we know that the total number of students in the class is 250 students.
So, we have the equation 5x = 250.
To solve for x, we divide both sides of the equation by 5:
x = 250/5 = 50.
Therefore, there are 50 seats in the band, and since each student chooses either band or choir, 50 students can choose band. Answer: \boxed{50}.