Use proportional relationships to solve this mixture problem. The incoming 6th-grade class has a choice between band or choir as an 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?(1 point) Responses 124 students 124 students 250 students 250 students 50 students 50 students 200 students
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.