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Question 177493: I am having difficulty solving this: The pupils in a certain class are divided equally into 3 groups A, B and C. The number of boys in A equals the number of girls in B. 25% of the boys in Class are in group C. What is the ratio of boys to girls?
I know that A and B are split equally with boys and girls. If group C has 25% of the boys that means the other 75% is split between the other 2 groups. This is where I get lost. Help please.
Thanks
Answer by gonzo(654)   (Show Source):
You can put this solution on YOUR website! you have 3 groups.
all 3 groups have the same number of students in them.
let y = the number of students in each group.
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let b = total number of boys in all 3 groups.
let g = total number of girls in all 3 groups.
since y equals the total number of students in each group, this means that the total number of students in all 3 groups is 3*y.
this also means that:
b + g = 3*y
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25% of the boys are in group C.
this means .25*b are in group C.
also means that 75% of the boys are in groups A and B.
which means that .75*b are in groups A and B.
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let x = number of boys in A.
that means the number of boys in B is equal to .75*b - x.
if the number of boys in B is accurate, then the number of boys in A and the number of boys in B should total .75*b
since x + .75*b - x = .75*b, this relationship holds and the number of boys in B is accurate.
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the number of boys in A equals the number of girls in B.
this means that the number of girls in B is equal to x.
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if the number of girls in B is x, and the number of boys in B is .75*b - x, and the total number of students in B is y, this means that:
.75*b - x + x = y
which means that:
.75*b = y
which means that:
b = y/.75
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you also have that:
b + g = 3*y
substituting y/.75 for b in that equation, you get:
y/.75 + g = 3*y
subtract y/.75 from both sides of this equation to get:
g = 3*y - y/.75
which makes:
g = 1.25*y/.75
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you have:
b = y/.75
g = 1.25*y/.75
this makes:
b + g = y/.75 + 1.25*y/.75 = 2.25*y/.75 = 3*y which is good because we already know that:
b + g = 3*y
the values of:
b = y/.75
g = 1.25*y/.75
have been confirmed to be good.
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since b = y/.75
and g = 1.25*y/.75
then the ratio of boys to girls must be:
b/g = (y/.75)/(1.25*y/.75)
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b/g = y/.75 / (1.25*y)/.75) is the same as:
b/g = y/.75 * (.75/1.25*y)
the .75 cancels out and the y cancels out and we are left with:
b/g = 1/1.25 which equals to .8
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the ratio of boys to girls is .8
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