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)
O 124 students
© 250 students
O 200 students
O50 students
Let's set up a proportion to solve this problem.
Let x be the number of students who choose band.
According to the problem, the number of seats in choir is four times the number of seats in band. So the number of students in choir is 4x.
The total number of students is 250, so we can write the equation:
x + 4x = 250
Combining like terms, we have:
5x = 250
Dividing both sides by 5, we find:
x = 50
Therefore, 50 students can choose band.
To solve this problem using proportional relationships, we need to set up a ratio between the number of seats in choir and band.
Given that there are four times as many seats in choir as there are in band, we can set up the following ratio:
Choir seats : Band seats = 4 : 1
Let's assume the number of seats in the band is x. Since there are four times as many seats in the choir, the number of seats in the choir would be 4x.
The total number of seats in both choir and band is 250, so we can write the equation:
x + 4x = 250
Simplifying the equation:
5x = 250
Dividing both sides by 5:
x = 50
Therefore, there are 50 seats in the band.
In order to solve this mixture problem using proportional relationships, we need to set up a ratio between the number of seats in choir and the number of seats in band.
Let's denote the number of seats in band as "b" and the number of seats in choir as "c". We are given that there are four times as many seats in choir as there are in band. This can be expressed as the equation:
c = 4b
We also know that the total number of students is 250. Therefore, the sum of the number of seats in band and choir should equal 250:
b + c = 250
Now we can substitute the value of "c" from the first equation into the second equation:
b + 4b = 250
Combining like terms, we simplify the equation to:
5b = 250
To solve for "b," we divide both sides of the equation by 5:
b = 250 / 5
Calculating this, we find:
b = 50
Therefore, the number of students that can choose band is 50.