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? 50 students 200 students 124 students 250 students​
Let's represent the number of seats in band as "x". 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 the sum of the number of students in band and choir, which is x + 4x = 5x.
We know that the total number of students is 250, so 5x = 250.
To solve for x, we divide both sides of the equation by 5: 5x/5 = 250/5.
This simplifies to x = 50.
Therefore, the number of students who can choose band is 50. Answer: \boxed{50}.
To solve this problem using proportional relationships, we can set up a ratio between the number of seats in band and choir.
Let x be the number of seats in band. Since there are four times as many seats in choir as in band, the number of seats in choir would be 4x.
Now, we can set up a proportion. The ratio of the number of seats in band to the total number of seats (band + choir) should be equal to the ratio of the number of students who can choose band to the total number of students.
x / (x + 4x) = students choosing band / total students
Simplifying the left side of the equation:
x / 5x = students choosing band / 250
Next, we can cross-multiply to solve for x:
x * 250 = 5x * students choosing band
250 = 5 * students choosing band
Dividing both sides of the equation by 5:
50 = students choosing band
Therefore, the number of students who can choose band is 50.
To solve this problem using proportional relationships, we can set up a proportion using the number of seats in band and choir.
Let's let x represent the number of seats in band. Since there are four times as many seats in choir as in band, the number of seats in choir would be 4x.
Now, we can set up the proportion:
x / (4x) = (number of students choosing band) / (total number of students)
Since the total number of students is given as 250, the proportion becomes:
x / (4x) = (number of students choosing band) / 250
To solve for x, we cross-multiply:
x * 250 = 4x * (number of students choosing band)
250x = 4x * (number of students choosing band)
Dividing both sides by 4:
62.5x = (number of students choosing band)
Since the number of students must be a whole number, the closest whole number to 62.5 is 62.
Therefore, the answer is that 62 students can choose band if there is a total of 250 students.