In a school ,the ratio of boys to girls is 9:4.if there are presently 720 girl students,how many more girls would it take to reduce the ratio of boys to girls 2:1?
what a lot of work! If there are presently 720 girls and 1620 boys, we need to add g girls such that
1620+g = 2(720+g)
g = 180
check: (1620+180):(720+180) = 1800:900 = 2:1
Yes, your calculation is correct. Apologies for the detailed explanation in the previous response.
If there are currently 720 girls and 1620 boys in the school, you would need to add 180 more girls to achieve a ratio of 2:1 (boys to girls). This is because 1620 (current number of boys) + 180 (additional girls) will equal 2 times the total number of girls in the school, which in this case is 720 (current number of girls) + 180 (additional girls).
Therefore, adding 180 more girls would indeed result in a ratio of 2:1 (boys to girls). Thank you for pointing out the simpler approach.
Given that the current ratio of boys to girls is 9:4 and there are currently 720 girl students, we can calculate the number of boys present in the school.
Let's assume there are 9x boys and 4x girls in the school. Since there are currently 720 girl students, we can set up an equation to find the value of x:
4x = 720
x = 720/4
x = 180
Now, we can find the number of boys in the school:
Number of boys = 9x = 9 * 180 = 1620
The total number of students in the school is the sum of the number of boys and girls:
Total number of students = 1620 + 720 = 2340
We want to reduce the ratio of boys to girls to 2:1. So, the new ratio would be 1:2 (since 2:1 is the inverse of 1:2). This means that for every boy, there would be 2 girls in the school.
If we let the number of additional girls needed be y, the total number of girls in the school would be 720 + y, and the total number of students in the school would be 2340 + y.
According to the new ratio, the total number of students would be evenly divisible by 3 (1 boy and 2 girls). So, we can set up the following equation:
(1620 + y) + (720 + y) = 3a
2340 + 2y = 3a
Since a is an integer, the total number of students must be evenly divisible by 3. Also, as we can see from the equation we get:
2y = 3a - 2340
To find the minimum value of y such that a is an integer, we need the smallest value that will make 2y a multiple of 3.
If we start with y = 1, we get:
2(1) = 3a - 2340
2 = 3a - 2340
3a = 2342
a = 2342/3 which is not an integer
If we try y = 2:
2(2) = 3a - 2340
4 = 3a - 2340
3a = 2344
a = 2344/3 which is not an integer
If we try y = 3:
2(3) = 3a - 2340
6 = 3a - 2340
3a = 2346
a = 2346/3 which is an integer
Therefore, we need at least 3 more girls to reduce the ratio of boys to girls to 2:1.