The music teacher would like to have the same number of girls and of boys in the chorus. She finds that 5/8 of the chorus are girls but that if she can get 10 more boys, the chorus will have the same number of boys as of girls.
(a) How many students are in the chorus?
(b) If there are 178 children in the school, which unit fraction would you select to represent the fraction of students in the present chorus? (Round the number of students in the chorus to the nearest ten. Round the number of students in the school to the nearest hundred.)
if 5/8 are girls, then 3/8 are boys
let the number of girls be 5x , and the number of boys be 3x
5x = 3x + 10
2x = 10
x = 5
number of girls is 25 and boys is 15
total in chorus is 40
fraction of chorus kids to whole student body
= 40/178 = 20/89
I don't get the point of the "unit fraction" calculation in this question.
As I understand it, a unit fraction has a 1 in the numerator, so
1/(89/20) = appr 1/4 ???
or appr 40/200 = 1/(200/40) = 1/5 if we round 178 to 200
your pick.
hjd
(a) To solve this problem, let's first determine the current number of boys in the chorus.
Let's assume the total number of students in the chorus is "x".
According to the given information, 5/8 of the chorus are girls. Therefore, the number of girls in the chorus is (5/8) * x.
Now, if the chorus has the same number of boys as girls, then the number of boys in the chorus should also be (5/8) * x.
But we are told that if she can get 10 more boys, the chorus will have the same number of boys as girls. So, the number of boys in the chorus should be [(5/8) * x] + 10.
Since the teacher wants the same number of boys and girls in the chorus, we can equate the number of boys to [(5/8) * x] + 10.
Therefore, [(5/8) * x] + 10 = (5/8) * x.
Now, let's solve this equation to find the value of "x".
[(5/8) * x] + 10 = (5/8) * x.
=> [(5/8) * x] - (5/8) * x = -10.
=> 0 = -10.
=> This equation has no solution.
It seems there is some discrepancy or error in the given information.
(b) Given the information provided is not sufficient to determine the number of students in the chorus or the unit fraction representing the fraction of students in the present chorus.
Let's solve the problem step-by-step:
(a) We can start by setting up an equation based on the given information. Let's assume the total number of students in the chorus is x.
According to the problem, 5/8 of the chorus are girls, which means there are (5/8)x girls in the chorus.
If the chorus has the same number of boys and girls when 10 more boys join, then the number of boys in the chorus would be (5/8)x + 10.
Since the teacher wants the same number of girls and boys, we can set up the equation:
(5/8)x = (5/8)x + 10
Now, let's solve for x:
Subtracting (5/8)x from both sides of the equation:
0 = 10
This equation doesn't give us any meaningful solution. It seems like there may be an error in the problem description.
(b) Since we couldn't find the number of students in the chorus based on the given information, we cannot find the unit fraction that represents the fraction of students in the present chorus.
To solve this problem, we need to use algebra. Let's assign variables to the unknown quantities:
Let x be the total number of students in the chorus.
Let y be the number of boys in the chorus.
Given that 5/8 of the chorus are girls, we know that (5/8)x are girls.
The problem states that if the music teacher can get 10 more boys, the number of boys will equal the number of girls. So, we have the equation:
y + 10 = (5/8)x
To find the total number of students in the chorus, we need to add the number of boys to the number of girls:
x = (5/8)x + y
We can now solve both equations simultaneously to find the values of x and y.
Substituting the value of y from the first equation into the second equation, we have:
x = (5/8)x + (y + 10)
Simplifying the equation, we get:
x = (5/8)x + (y + 10)
x - (5/8)x = y + 10
(3/8)x = y + 10
3x = 8(y + 10)
Now, we can substitute the value of y in terms of x from the first equation into the second equation:
3x = 8((5/8)x + 10)
3x = 5x + 80
3x - 5x = 80
-2x = 80
x = -40
Since the number of students cannot be negative, there is no solution for x. This means the problem is contradictory, and there is no possible scenario that satisfies the given conditions.
Let's move on to part (b) of the question.
If there are 178 children in the school, and we are asked to round the number of students in the chorus to the nearest ten, we need to find a unit fraction that represents the fraction of students in the chorus.
Since we found that there is no solution for the number of students in the chorus in part (a), we cannot determine the exact fraction. However, we can still approximate it.
Rounding 178 to the nearest hundred, we have 200. Since we don't have an exact number for the students in the chorus, we will use an approximation. We can select the nearest unit fraction based on our approximation. In this case, since there are 200 students in the school and no solution for the chorus, we can say the fraction of students in the chorus is 0/200.
Please note that this is an estimation based on rounding, as there is no exact determination for the number of students in the chorus.