Question

Question

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)
Responses

124 students
124 students

50 students
50 students

200 students
200 students

250 students
250 students

Answer 1

To solve this problem, let's use a proportional relationship.

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

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:

\[ b + 4b = 250 \]

This simplifies to:

\[ 5b = 250 \]

Now, we can solve for \( b \):

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

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