There are 36 students in a student council in a school and the ratio of the number of boys to girls is 3:1 . How many more girls should be added to the council so that the ratio of boys to the number of girls may be 9:5
To solve this problem, we need to find the number of boys and girls in the student council, and then determine how many girls should be added to achieve the desired ratio.
Given that the ratio of boys to girls is 3:1, we can represent it as 3x:1x, where x is a constant factor.
We know that there are 36 students in total, so the sum of the constant factors, 3x + 1x, must add up to 36:
3x + 1x = 36
Combining like terms, we have:
4x = 36
To solve for x, we divide both sides of the equation by 4:
x = 36/4
x = 9
Now we can find the number of boys and girls in the student council:
Number of boys = 3x = 3 * 9 = 27
Number of girls = 1x = 1 * 9 = 9
To achieve the desired ratio of 9:5 (boys to girls), we need to determine how many more girls should be added.
Let's assume that we need to add 'y' girls to the council to achieve this ratio.
So, the new number of girls would be 9 + y, and the new number of boys would remain 27.
The new ratio of boys to girls would then be 27:(9 + y), which is equivalent to 9:5.
Now, we can set up an equation to solve for 'y':
27/(9 + y) = 9/5
Cross-multiplying, we get:
27 * 5 = 9 * (9 + y)
Simplifying, we have:
135 = 81 + 9y
Moving the terms around, we get:
9y = 135 - 81
9y = 54
Dividing both sides by 9, we find:
y = 54/9
y = 6
Therefore, we need to add 6 more girls to the council in order to achieve the desired ratio of 9:5 (boys to girls).
36 students
B:G = 3:1 = 27 : 9
Add x girls,
27/(9+x)=9/5
Solve for x by cross multiplication.