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
250 students
250 students
50 students
50 students
124 students
124 students
200 students
The correct answer is: 50 students.
If there are four times as many seats in choir as there are in band, and the total number of seats is 250, we can set up a proportional relationship:
Band seats : Choir seats = 1 : 4
Let's represent the number of band seats as x. The number of choir seats would then be 4x.
x + 4x = 250
5x = 250
x = 50
Therefore, there are 50 band seats available for students to choose from.
To solve this mixture problem using proportional relationships, we need to find the number of seats in band and choir.
Let's assume the number of seats in band is "x."
According to the problem, there are four times as many seats in choir as in band. So, the number of seats in choir is 4x.
Now, we know that the total number of students is 250.
Using the proportional relationship, we can set up the equation:
x + 4x = 250
Combining like terms, we get:
5x = 250
Dividing both sides of the equation by 5, we find:
x = 50
Therefore, there are 50 seats in band, and we can conclude that 50 students can choose band as their elective.
To solve this mixture problem using proportional relationships, we need to compare the number of seats in band and choir.
Given that there are four times as many seats in choir as there are in band, we can set up the following proportion:
Seats in choir / Seats in band = 4
Let's assume the number of seats in band is x. Then the number of seats in choir would be 4x.
Now, we can add the number of seats in band and choir to find the total number of students:
x + 4x = 250
Simplifying the equation:
5x = 250
Dividing both sides of the equation by 5:
x = 50
Therefore, there are 50 seats in band, which means 50 students can choose band as their elective.
So, the correct answer is:
50 students