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
200 students
200 students
50 students
50 students
250 students
The ratio of choir seats to band seats is 4:1. This means that for every 4 choir seats, there is 1 band seat.
Since the total number of seats is 250, we can set up the equation:
4x + x = 250
Simplifying the equation:
5x = 250
Dividing both sides by 5:
x = 50
Therefore, there are 50 band seats available.
The correct answer is:
50 students
To solve this mixture problem, let's use the concept of proportional relationships.
Let x be the number of seats in band. Since there are four times as many seats in choir as there are in band, the number of seats in choir can be represented as 4x.
The total number of students in the incoming 6th-grade class is given as 250. Since each student can choose either band or choir, the total number of students should be equal to the sum of the students in band and choir.
So, the equation representing this situation is:
x + 4x = 250
Combining like terms, we get:
5x = 250
To solve for x, divide both sides of the equation by 5:
x = 250 / 5
x = 50
Therefore, there are 50 students who can choose band as their elective.
To solve this mixture 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 write the ratio as:
Choir seats : Band seats = 4 : 1
Next, we need to find the number of students that can choose band if there is a total of 250 students. We'll assume that every student will choose either band or choir.
To find the number of students that can choose band, we'll set up another ratio using the proportion:
Band students : Total students = Band seats : Total seats
We know that the ratio of Band seats to Total seats is 1 : 5 (since there are 4 seats for choir and 1 seat for band, making a total of 5 seats). Therefore, our new ratio becomes:
Band students : 250 = 1 : 5
To solve for Band students, we can cross-multiply the ratios:
1 * 250 = Band students * 5
Simplifying the equation, we get:
250 = 5 * Band students
Dividing both sides of the equation by 5, we find:
Band students = 50
Hence, the answer is 50 students can choose band as their elective.