SOLUTION: In a High school there are two Form 5 classes with the same number of students in each. The ratio of girls to boys in one Form 5 is 1 : 2 and in the other Form it is 3 : 2. What

Question 1082382: In a High school there are two Form 5 classes with the same number of students
in each. The ratio of girls to boys in one Form 5 is 1 : 2 and in the other Form it is 3 : 2. What is the ratio of girls to boys in the entire Form 5?

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
you've got 2 form 5 classes with the same number of students in each class.

the ratio of girls to boys in each class is:

first form 5 class = 1:2
second form 5 class = 3:2

a ratio of 1:2 means that there is 1 girl for every 2 boys in the first form 5 class.
this means that there is 1 girl out of 3 students in the first form 5 class.

a ratio of 3:2 means that there are 3 girls for every 2 boys in the second form class.
this means that there are 3 girls out of 5 students in the second form class.

therefore the ratio of girls to students in the first form 5 class is 1/3.
therefore the ratio of girls to students in the second form 5 class is 3/5.

if you let x equal the number of students in each class, then:

the number of girls in the first form 5 class is 1/3 * x.
the number of girls in the second form 5 class is 3/5 * x.

the total number of students in both classes is 2x.
the total number of girls in both classes is 1/3 * x + 3/5 * x.

1/3 is equivalent to 5/15.
3/5 is equivalent to 9/15.

the total number of girls in both classes is therefore equal to 5/15 * x + 9/15 * x = 14/15 * x.

since the total number of students in both classes is equal to 2x, then:

the ratio of girls to students in both classes is equal to (14/15 * x) / 2x.
simplify to get the ratio of girls to students in both classes is equal to 7/15 * x.

this means that there are 7 girls for every 15 students.
this means that 8 of those 15 students have to be boys.

the ratio of girls to boys in both classes is therefore 7/8.

to see if this makes sense, let's use numbers.

assume the number of students in each class is 45.
this means the number of students in both classes is 90.

in the first form 5 class, the ratio of girls to boys is 1:2.
this means that there is 1 girl for every 3 students and 2 boys for every 3 students.
divide 45 by 3 and you get 15.
this means you have 15 groups of 3 in the first form 5 class.
within each of these groups of 3, 1 of them are girls and 2 of them are boys.
this means in the total class of 45 you have 1 * 15 = 15 girls and 2 * 15 = 30 boys.

in the second form 5 class the ratio of girls to boys is 3:2.
this means that there are 3 girls for every 5 students and 2 boys for every 5 students.
divide 45 by 5 and you get 9.
this means you have 9 groups of 5 in the second form 5 class.
within each of these groups of 5, 3 are girls and 2 are boys.
this means in the total class of 45 you have 3 * 9 = 27 girls and 2 * 9 = 18 boys.

in the first class you have 15 girls and 30 boys.
in the second class you have 27 girls and 18 boys.

the total girls in both classes is 15 + 27 = 42.
the total boys in both classes is 30 + 18 = 48.

the ratio of girls to boys in both classes is 42/48 = 21/24 = 7/8.

looks like we calculated the ratio correctly since this agrees with what we got before.

the ratio of girls to students in both classes would be 42/90 = 21/45 = 7/15.

this also agrees with what we got earlier when we were using x instead of 45.

your solution is that the ratio of girls to boys in the entire form 5 class is 7:8.

there are 7 girls for every 8 boys in both classes.

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