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
200 students
200 students
250 students
250 students
50 students
50 students
124 students
To solve this problem using proportional relationships, we can set up a proportion between the number of seats in band and choir:
Seats in choir/Seats in band = Number of students in choir/Number of students in band
We are given that there are four times as many seats in choir as there are in band. Therefore, the proportion becomes:
4/1 = Number of students in choir/Number of students in band
We also know that there is a total of 250 students, so the number of students in choir + number of students in band = 250.
Using this information, we can set up another proportion:
Number of students in choir + Number of students in band = 250
Number of students in choir/Number of students in band = 4/1
Simplifying the proportion, we get:
(Number of students in choir)/(Number of students in band) = 4
Cross-multiplying, we get:
4 * Number of students in band = Number of students in choir
Substituting the second proportion into the first equation, we get:
(Number of students in band) + 4 * Number of students in band = 250
Combine like terms:
5 * (Number of students in band) = 250
Divide both sides by 5:
(Number of students in band) = 50
Therefore, there are 50 students who can choose band.
To solve this problem, we can set up a proportional relationship between the number of seats in the band and choir.
Let's assume the number of seats in the band is "x". According to the problem, there are four times as many seats in the choir as there are in the band. So, the number of seats in the choir is 4x.
Since there are a total of 250 students, the number of students choosing the band plus the number of students choosing the choir should equal 250.
Therefore, we can set up the following equation:
x + 4x = 250
Combining like terms, we have:
5x = 250
Dividing both sides of the equation by 5, we get:
x = 50
Thus, there are 50 seats in the band, so 50 students can choose the band as their elective. Therefore, the correct answer is:
50 students
To solve this mixture problem using proportional relationships, we need to understand the relationship between the number of seats in choir and band. Given that there are four times as many seats in choir as in band, we can set up a proportion to find the number of students who can choose band.
Let x be the number of seats in band.
According to the problem, the number of seats in choir is four times the number of seats in band. Therefore, the number of seats in choir is 4x.
The total number of students is 250, so we can set up the following proportion:
x / (4x) = 250 / 1
To solve this proportion, we can cross-multiply:
1 * x = 250 * (4x)
Simplifying the equation, we have:
x = 1000x
Dividing both sides by x, we get:
1 = 1000
This is a contradiction, which means that there is no value of x that satisfies the proportion. Therefore, there is no solution to the problem using proportional relationships.
In conclusion, we cannot determine the number of students who can choose band using the given information and proportional relationships.