Use proportional relationships to solve this mixture problem the incoming sixth grade class has a choice between band or choir as an elective. There are four times any seats in the choir as there are in band how many students can choose band if there’s a total of 250 students.

Answer 1

To solve the problem using proportional relationships, let's define some variables for the number of students in each elective:

• Let \( b \) represent the number of students in band.
• Since there are four times as many seats in the choir as there are in band, the number of students in choir will be \( 4b \).

According to the problem, the total number of students in both band and choir is 250. This gives us the equation:

\[ b + 4b = 250 \]

Now we can combine like terms:

\[ 5b = 250 \]

Next, we solve for \( b \):

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

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

To find the number of students in choir, we can substitute \( b \) back into the expression for choir:

\[ 4b = 4 \times 50 = 200 \]

The total is indeed \( 50 + 200 = 250 \), which confirms our solution is correct. Thus, 50 students can choose band, and the answer is \( \boxed{50} \).