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
200 students
124 students
250 students
50 students
To solve this problem using proportional relationships, we need to set up a ratio between the number of students in band and the number of students in choir.
Let the number of students in band be x. Since there are four times as many seats in choir as there are in band, the number of students in choir would be 4x.
The total number of students is given as 250, so we can set up the equation:
x + 4x = 250
Combining like terms:
5x = 250
Dividing both sides by 5:
x = 50
Therefore, the number of students that can choose band is 50. Hence, the correct answer is:
50 students
Carla needs to complete her science homework. She has 20 pages to read and 14 questions to answer. If it takes Carla 10 minutes to read 4 pages, how many minutes will it take her to read the full assignment?(1 point)
Responses
35 minutes
9 minutes
85 minutes
50 minutes
To solve this problem, we can use proportional relationships.
If Carla can read 4 pages in 10 minutes, we can set up a ratio:
4 pages / 10 minutes = 20 pages / x minutes
Cross-multiplying, we get:
4x = 10 * 20
4x = 200
Dividing both sides by 4, we find:
x = 50
Therefore, it will take Carla 50 minutes to read the full assignment. Hence, the correct answer is:
50 minutes
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To solve this problem, we can set up a proportional relationship between the number of students in choir and the number of students in band.
Let's call the number of students in choir "C" and the number of students in band "B".
According to the problem, there are four times as many seats in choir as there are in band. This means that the ratio of the number of students in choir to the number of students in band is 4:1.
We can set up the following proportion:
C/B = 4/1
Next, we know that the total number of students is 250, so we can set up another proportion:
C + B = 250
Now, let's solve these proportions:
From the first proportion, we can cross-multiply:
C = 4B
Substituting this into the second proportion:
4B + B = 250
Simplifying:
5B = 250
Dividing both sides by 5:
B = 50
Therefore, the number of students who can choose band is 50.
Therefore, the correct answer is:
50 students
To solve this mixture problem using proportional relationships, we need to set up a proportion between the number of seats in the band and choir.
Let's represent the number of seats in the band as 'b' and the number of seats in the choir as 'c'. According to the problem, there are four times as many seats in choir as there are in the band. So we can write the proportion as:
c/b = 4/1
Now, we also know that the total number of students is 250. So the sum of the number of seats in the band and choir should be equal to 250:
b + c = 250
To find the number of students who can choose the band, we need to solve these two equations simultaneously.
Let's start by solving the proportion:
c/b = 4/1
Cross multiplying:
c = 4b
Now substitute this value of 'c' in the second equation:
b + 4b = 250
Combining like terms:
5b = 250
Dividing both sides by 5:
b = 50
So the number of students who can choose the band is 50.
Therefore, the correct answer is:
50 students.