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?(
To solve this mixture problem using proportional relationships, we need to set up a proportion based on the given information.
Let's define:
x = number of seats in band
4x = number of seats in choir
Now, we can set up the proportion:
x / (4x) = number of students in band / total number of students
Cross-multiplying the proportion, we get:
x = (number of students in band / total number of students) * 4x
Simplifying, we have:
x = (number of students in band) * 4
Since there are a total of 250 students, we can substitute this into the equation:
x = (number of students in band) * 4 = 250
Dividing both sides by 4, we get:
(number of students in band) = 250 / 4 = 62.5
Since we cannot have a fraction of a student, the number of students in band must be a whole number. Therefore, the closest whole number to 62.5 is 63.
So, if there are a total of 250 students, 63 students can choose band as their elective.
Let's assume the number of seats in band is x.
According to the problem, the number of seats in choir is four times that of band, thus the number of seats in choir is 4x.
The total number of students is 250. So the number of students in band plus the number of students in choir is 250.
According to the proportional relationship, the ratio of the number of students in band to the number of students in choir is equal to the ratio of the number of seats in band to the number of seats in choir.
We can set up the equation:
x / 4x = #students in band / #students in choir
Cross-multiply to get:
x * #students in choir = 4x * #students in band
Simplify to get:
#students in choir = 4 * #students in band
Since there are 250 students in total, the number of students in choir plus the number of students in band is 250.
Thus, #students in choir + #students in band = 250
Substituting the value of #students in choir from the previous equation:
4 * #students in band + #students in band = 250
Simplify to get:
5 * #students in band = 250
Divide both sides by 5 to solve for the number of students in band:
#students in band = 250 / 5 = 50
Therefore, 50 students can choose band as their elective.
To solve this mixture problem using proportional relationships, we need to set up a proportion based on the given information and then solve for the unknown variable.
Let's represent the number of seats in band as "b" and the number of seats in choir as "c".
According to the problem, there are four times as many seats in choir as there are in band. Therefore, we can write the proportion:
c / b = 4
We also know that the total number of students is 250. So, the sum of the number of students in band and choir should equal this total:
b + c = 250
To solve for the number of students who can choose band, we need to find the value of "b".
To do that, we can use substitution. Since we have the equation c / b = 4, we can rearrange it to get c = 4b.
Now, substitute this value of c into the second equation:
b + 4b = 250
Combining like terms, we get:
5b = 250
Divide both sides of the equation by 5:
b = 50
Hence, there are 50 seats available for band, so 50 students can choose band as their elective.