Use proportional relationships to solved 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?
Options:
200 students
124 students
259 students
50 students
Let's assume the number of seats in the band is "x". Since the number of seats in choir is 4 times the number of seats in the band, the number of seats in choir would be 4x.
According to the problem, the total number of students is 250. So, the number of students who can choose band would be x.
We can set up a proportion to solve for x:
x/4x = 250/1
Cross-multiplying, we get:
1 * x = 4x * 250
x = (4x * 250)/1
x = 1000x
Dividing both sides by x:
1 = 1000
This is not possible, so there is no solution that satisfies the given conditions.
Therefore, none of the given options (200 students, 124 students, 259 students, 50 students) are correct.
Which one
Apologies for the confusion. It seems that I made an error in my calculations.
Let's approach the problem again:
We know that there are four times as many seats in choir as there are in the band. Let's say the number of seats in the band is "x". Therefore, the number of seats in the choir would be 4x.
We also know that the total number of students is 250.
To find out how many students can choose band, we need to determine the value of x.
Since the ratio of the number of seats in choir to the number of seats in the band is 4:1, we can set up the following proportion:
4x/x = 250/1
Cross-multiplying, we get:
4x = 250
Dividing both sides by 4:
x = 250/4
x = 62.5
We can't have a fraction of a seat, so we need to round down to the nearest whole number:
x = 62
Therefore, the number of students that can choose band is 62.
Among the given options (200 students, 124 students, 259 students, 50 students), the closest one is 50 students. So the correct option is:
50 students
Let's set up a proportion to solve this problem.
Let x be the number of seats in the band.
According to the problem, the number of seats in the choir is four times the number of seats in the band. So the number of seats in the choir is 4x.
The total number of students is 250, so the sum of the number of band seats and choir seats is 250.
x + 4x = 250
Combining like terms, we get:
5x = 250
Dividing both sides by 5, we find:
x = 50
Therefore, there are 50 students who can choose band.
The correct answer is: 50 students.
To solve this mixture problem using proportional relationships, we need to compare the number of seats in the band and choir to find the number of students that can choose band.
Given that there are four times as many seats in choir as there are in band, we can set up a proportion:
Number of choir seats / Number of band seats = Number of choir students / Number of band students
Let's assign variables:
Let B represent the number of band seats.
Let C represent the number of choir seats.
Let x represent the number of band students.
Let y represent the number of choir students.
Based on the information given, we know that C = 4B (there are four times as many choir seats as band seats), and x + y = 250 (the total number of students).
Now let's substitute the values into the proportion and solve for x:
C / B = y / x
(4B) / B = (y) / x
4 = y / x
Now, we substitute y = 250 - x into the equation:
4 = (250 - x) / x
Multiplying both sides by x:
4x = 250 - x
Adding x to both sides:
5x = 250
Dividing both sides by 5:
x = 50
So, the number of students that can choose band is 50.
Therefore, the correct answer is 50 students.