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Since there are four times as many seats in choir as there are in band, we can set up a proportion:
Band Seats / Choir Seats = Band Students / Choir Students
Let's use x as the number of students choosing band.
x / (4x) = x / (250-x)
Cross-multiplying:
x * (250-x) = x * (4x)
250x - x^2 = 4x^2
Rearranging the equation:
5x^2 - 250x = 0
Factoring out x:
x * (5x - 250) = 0
Setting each factor equal to zero:
x = 0 or 5x - 250 = 0
Since we can't have zero students choosing band, we solve for x in the second equation:
5x - 250 = 0
5x = 250
x = 50
Therefore, 50 students can choose band.