Use proportional relationship to solve this Mixture problem. The incoming six grade class has a choice between band choir as an elective. There are four times as many seats inquire as there are in band how many students can choose band if there is a total of 250 students.

Answer 1

Let's denote the number of seats in band as \( b \) and the number of seats in choir as \( c \). According to the problem, we have the following relationships:

1. The number of seats in choir is four times the number of seats in band: \[ c = 4b \]

2. The total number of students is 250. This can be represented by the equation: \[ b + c = 250 \]

Now we can substitute the first equation into the second. Replacing \( c \) with \( 4b \) gives us: \[ b + 4b = 250 \]

Now combine like terms: \[ 5b = 250 \]

To find \( b \), divide both sides by 5: \[ b = \frac{250}{5} = 50 \]

Now that we have the value of \( b \), we can find the number of seats in choir \( c \) using the first relationship: \[ c = 4b = 4 \times 50 = 200 \]

Thus, the final answer is:

• The number of students who can choose band is 50.
• The number of students who can choose choir is 200.