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)
250 students
200 students
124 students
50 students
Pick an answer CHOICE.
According to the information given, the number of seats in choir is four times the number of seats in band. Therefore, the ratio of the number of seats in choir to the number of seats in band is 4:1.
To solve the problem, we can set up the proportion:
Number of seats in choir / Number of seats in band = 4 / 1
Let's represent the number of seats in band as x. Therefore, the number of seats in choir is 4x.
Since the total number of students is 250, we can set up another proportion:
Number of students in choir / Number of students in band = (Number of seats in choir) / (Number of seats in band)
Number of students in choir / Number of students in band = (4x) / x
Number of students in choir / Number of students in band = 4
Now, let's substitute the total number of students into the second proportion:
Number of students in choir / Number of students in band = 4
Number of students in choir / x = 4
Number of students in choir = 4x
Since the total number of students is 250, we can substitute this information into the equation:
250 / x = 4
Cross multiplying, we get:
4x = 250
Dividing both sides by 4, we find:
x = 62.5
Since we can't have a fraction of a student, we must round the answer down to the nearest whole number. Therefore, the number of students that can choose band is 62.
So, the correct answer is 50 students.
To solve this problem using proportional relationships, we need to set up a ratio between the number of seats in band and the number of seats in choir.
Let's call the number of seats in band "b" and the number of seats in choir "c."
According to the problem, there are four times as many seats in choir as there are in band. This can be represented as the proportion:
c/b = 4/1
To find the number of students who can choose band, we need to determine the value of "b."
Since we know the total number of students is 250, we can set up another proportional relationship to relate the total number of students to the number of seats in band:
c + b = 250
Substituting the value of c from the first equation into the second equation:
b + (4b) = 250
5b = 250
b = 250/5
b = 50
Therefore, there are 50 students who can choose band. The correct answer is "50 students."
To solve this problem using proportional relationships, we need to set up a ratio between the number of seats in choir and the number of seats in band. In this case, it is given that there are four times as many seats in choir as there are in band.
Let's assume the number of seats in band = x.
The number of seats in choir = 4x.
Total number of students = 250.
Now we can set up a proportion:
(x seats in band) : (4x seats in choir) = (number of students in band) : (number of students in choir)
We are asked to find the number of students who can choose band, which is the number of students in the band.
To solve for x, we can cross-multiply the proportion:
x * number of students in choir = 4x * number of students in band
Since the total number of students is 250, we can substitute it into the equation:
x * (250 − x) = 4x * number of students in band
Expanding the equation further:
250x − x^2 = 4x * number of students in band
Now, we need to solve this quadratic equation to find the value of x.
To solve for x, let's rearrange the equation:
x^2 − 250x + 4x * number of students in band = 0
Based on the answer choices provided, we can substitute each value and check which one satisfies the equation:
- 250 students:
(250)^2 − 250 * 250 + 1000 * 250 = 0
62500 − 62500 + 250000 = 0
0 = 0
- 200 students:
(200)^2 − 250 * 200 + 1000 * 200 = 0
40000 − 50000 + 80000 = 0
0 = 0
- 124 students:
(124)^2 − 250 * 124 + 1000 * 124 = 0
15376 − 31000 + 124000 = 0
0 ≠ 0
- 50 students:
(50)^2 − 250 * 50 + 1000 * 50 = 0
2500 − 12500 + 50000 = 0
0 = 0
From the calculations, we see that the only answer choice that satisfies the equation is:
The number of students who can choose band = 200 students.
Therefore, the answer is:
200 students.