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?(
Let's represent the number of seats in band as x.
According to the problem, the number of seats in choir is four times the number of seats in band, so we can represent the number of seats in choir as 4x.
The total number of students is 250, so the sum of the number of students in band and choir is x + 4x = 250.
Combining like terms, we get 5x = 250.
Dividing both sides of the equation by 5, we find that x = 50.
Therefore, there are 50 seats in band, so 50 students can choose band. Answer: \boxed{50}.
To solve this mixture problem using proportional relationships, we can set up a ratio between the number of seats in band and the number of seats in choir.
Let's assume the number of seats in band is "x." According to the given information, there are four times as many seats in choir as in band. Therefore, the number of seats in choir is 4x.
We know that the total number of students is 250. So, the equation becomes:
x + 4x = 250
To solve for x, we can combine like terms:
5x = 250
To isolate x, divide both sides of the equation by 5:
x = 250/5
Simplifying, we find:
x = 50
Therefore, there are 50 seats in the band, and this means that 50 students can choose band as their elective.
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 there are in band, we can set up the following proportion:
x/4x = C/B
Where:
x is the number of seats in band,
4x is the number of seats in choir,
C is the number of students choosing choir, and
B is the number of students choosing band.
We are given that the total number of students is 250, so we can set up another proportion:
C + B = 250
Now we can solve for the number of students choosing band (B).
Let's start with the second proportion:
C + B = 250
Since C = 4x, we can substitute it into the equation:
4x + B = 250
Now we can solve for B:
B = 250 - 4x
Now let's substitute this value of B into the first proportion:
x/4x = C/B
x/(4x) = (4x)/(250 - 4x)
Now we can cross-multiply:
x(250 - 4x) = 4x * 4x
250x - 4x^2 = 16x^2
20x^2 - 250x = 0
Divide through by 10x:
2x - 25 = 0
Now solve for x:
2x = 25
x = 12.5
Since x represents the number of seats in band, it cannot be a fraction. Therefore, we round it up to the nearest whole number:
x = 13
So, there are 13 seats in the band. Now we can substitute this value back into one of the equations to find the number of students choosing band:
B = 250 - 4x
B = 250 - 4(13)
B = 250 - 52
B = 198
Therefore, 198 students can choose band.