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)Responses50 students50 students250 students250 students124 students124 students200 students
If there are four times as many seats in choir as there are in band, and the total number of students is 250, we can set up a proportion:
Band seats/Choir seats = Band students/Choir students
Let's represent the number of band seats as x and the number of choir seats as 4x. Since the total number of students is 250, the total number of band students and choir students combined is 250:
x + 4x = 250
Combining like terms:
5x = 250
Dividing both sides of the equation by 5:
x = 50
Therefore, there are 50 students who can choose band as an elective.
To solve this problem using proportional relationships, we can set up a proportion to find the number of students who can choose band.
The ratio of the number of seats in band to choir is 1:4. This means that for every 1 seat in band, there are 4 seats in choir.
Let's represent the number of seats in band as 'x'. The number of seats in choir can be represented as 4x because there are 4 times as many seats in choir.
Since the total number of students is 250, we can write the following equation:
x + 4x = 250
Combining like terms:
5x = 250
To solve for x, divide both sides of the equation by 5:
x = 250/5
Simplifying:
x = 50
So, there are 50 seats in the band. Therefore, 50 students can choose band as an elective.
To solve this mixture problem using proportional relationships, we need to compare the number of seats in choir to the number of seats in band.
Let's assume the number of seats in band is x.
Since there are four times as many seats in choir as in band, the number of seats in choir would be 4x.
The total number of seats available for both band and choir would be x + 4x = 5x.
Given that the total number of students is 250, we can set up the following proportion:
(x + 4x) / 5x = 250 / 1
Simplifying the left side of the equation:
5x / 5x = 1
Therefore, x = 1.
Now we can find the number of students who can choose band by substituting x back into the equation:
x = 1
So, the number of students who can choose band is 1 x 250 = 250 students.
Therefore, the correct answer is 250 students.