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)
250 students
200 students
124 students
50 students
Since there are four times as many seats in choir as there are in band, and we know the total number of students is 250, we can set up the following proportion:
x (number of students in band) / 4x (number of students in choir) = 1/4 (proportion of seats in band to choir)
To solve for x, we can cross-multiply:
4x = 1/4 * 250
4x = 62.5
x = 62.5 / 4
x ≈ 15.625
Since we can't have a fraction of a student, we round down to the nearest whole number:
x ≈ 15
Therefore, approximately 15 students can choose band as their elective.
To solve this problem, we can use a proportional relationship between the number of seats in choir and band.
Let's say the number of seats in band is represented by "b" and the number of seats in choir is represented by "c."
Given that there are four times as many seats in choir as in band, we can write the proportion:
c/b = 4/1
Since the total number of students is 250, the sum of the number of seats in choir and band must equal 250:
c + b = 250
Now we can solve this system of equations to find the value of b:
From the proportion, we can solve for c:
c/b = 4/1
c = 4b
Substitute this expression for c into the second equation:
4b + b = 250
5b = 250
b = 250/5
b = 50
Therefore, the number of students that can choose band is 50.
To solve this mixture problem using proportional relationships, we need to set up a proportion between the number of seats in band and choir.
Let's assume the number of seats in band is "x". According to the information given, the number of seats in choir is four times the number of seats in band, so 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
To find the number of students who can choose band, we need to solve for x in the proportion.
x/(4x) = "number of students choosing band"/250
Cross multiplying gives us:
250 * x = 4x * "number of students choosing band"
Simplifying, we get:
250 = 4 * "number of students choosing band"
Dividing both sides by 4, we get:
"number of students choosing band" = 250/4
"number of students choosing band" = 62.5
Since the number of students must be a whole number, we round down to the nearest whole number:
"number of students choosing band" = 62 students
Therefore, the correct answer is 62 students can choose band.