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)

Question

Responses

250 students
250 students

124 students
124 students

50 students
50 students

200 students .

Answer 1

Let the number of students choosing band be \( b \) and the number of students choosing choir be \( c \).

According to the problem, we know two things:

1. The total number of students is 250: \[ b + c = 250 \]
2. There are four times as many seats in choir as there are in band: \[ c = 4b \]

Now we can substitute the second equation into the first equation: \[ b + 4b = 250 \]

Combining like terms gives: \[ 5b = 250 \]

Now, divide both sides by 5: \[ b = \frac{250}{5} = 50 \]

Thus, the number of students that can choose band is 50 students.

The correct response is: 50 students.