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

50 students
50 students

250 students
250 students

200 students

Answer 1

Let \( b \) be the number of students who choose band, and \( c \) be the number of students who choose choir. According to the problem, we have the following relationships:

1. There are four times as many seats in choir as there are in band: \[ c = 4b \]

2. The total number of students choosing band or choir is 250: \[ b + c = 250 \]

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

\[ b + 4b = 250 \]

This simplifies to:

\[ 5b = 250 \]

Next, solving for \( b \):

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

Thus, the number of students who can choose band is \( \boxed{50} \).