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

124 students
124 students

250 students
250 students

50 students
50 students

200 students

Answer 1

Let's define the number of seats in band as \( b \) and the number of seats in choir as \( c \). According to the problem, we know that:

1. \( c = 4b \) (There are four times as many seats in choir as in band)
2. The total number of seats available is 250: \( b + c = 250 \)

Now, we can substitute the first equation into the second equation:

\[ b + 4b = 250 \]

This simplifies to:

\[ 5b = 250 \]

Now, divide both sides by 5:

\[ b = \frac{250}{5} = 50 \]

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

Thus, the correct answer is:

50 students.