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)
200 students
250 students
124 students
50 students
To solve this problem using proportional relationships, we can set up a proportion comparing the number of seats in choir to the number of seats in band.
Let's represent the number of seats in choir as "C" and the number of seats in band as "B".
We know that there are four times as many seats in choir as there are in band, so we can write the following proportion:
C/B = 4/1
If we can find the value of C, we can then subtract it from the total number of students to find the number of students who can choose band.
To solve the proportion, we can cross multiply:
C = 4B
Since we know that the total number of students is 250, we can write the following equation:
C + B = 250
Substituting the value of C from the proportion into the equation:
4B + B = 250
5B = 250
Dividing both sides of the equation by 5:
B = 50
Therefore, the number of students who can choose band is 50.
The correct answer is:
50 students.
To solve this problem using proportional relationships, you can set up a ratio between the number of seats in choir and band:
Number of choir seats : Number of band seats
Since there are four times as many seats in choir as there are in band, the ratio can be expressed as:
4 : 1
To find the number of students who can choose band, you can use the proportion:
(Number of students choosing band) / (Total number of students) = (Number of band seats) / (Total number of seats)
Given that there are 250 students in total and the ratio of choir seats to band seats is 4:1, we can substitute these values into the proportion:
(Number of students choosing band) / 250 = 1 / (4 + 1)
(Number of students choosing band) / 250 = 1/5
By cross multiplying, we can solve for the number of students choosing band:
(Number of students choosing band) = 250 * (1/5)
(Number of students choosing band) = 50
Therefore, the answer is:
50 students.
To solve this problem using proportional relationships, we need to understand that the ratio between the number of seats in choir and band is 4:1.
First, let's find out the number of seats in band. If there are four times as many seats in choir as there are in band, we can set up the proportion:
(number of seats in choir) : (number of seats in band) = 4 : 1
Let x represent 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 would be 4x.
The total number of students is given as 250. Therefore, the number of students who choose band plus the number of students who choose choir would be equal to 250.
Students choosing band + Students choosing choir = Total number of students
x + 4x = 250
Now we can solve this equation to find the value of x:
5x = 250
x = 250/5
x = 50
So there are 50 seats in band, and therefore, 50 students can choose band as their elective.
Therefore, the correct answer is:
50 students