# Thread: Fraction of girls??

1. ## Fraction of girls??

There are three Secondary 1 classes. The number of students in each of the three classes is the same. The fraction of girls in Secondary 1A is the same as the fraction of boys in Secondary 1C. 1/5 of all Secondary boys are in Secondary 1B. What fraction of the total number of Secondary 1 students are girls?

Thank you if you can help me with this problem!!

2. Hello, acc100jt!

Two problems:

[1] Is there a typo?
. . .Is the question "What fraction of Secondary 2 are girls?"

[2] The designations are far too confusing; I'll simplify the wording.

There are three classes: $A,\:B,\:C.$
The number of students in each of the three classes is the same.
The fraction of girls in $A$ is the same as the fraction of boys in $C.$
$\frac{1}{5}$ of all boys are in $B.$

What fraction of the B students are girls?

Let $N$ = number of students in each class.

$A\!: \begin{array}{cc}a & \text{girls} \\ N-a & \text{boys}\end{array}\qquad
B\!:\begin{array}{cc}b & \text{girls} \\ N-b & \text{boys}\end{array}\qquad
C\!:\begin{array}{cc}c &\text{girls} \\ N-c & \text{boys}\end{array}
$

"The fraction of girls in $A$ is the same as the fraction of boys in $C$."
. . $\frac{a}{N}\:=\:\frac{N-c}{N}\quad\Rightarrow\quad a\:=\:N-c\quad\Rightarrow\quad a + c\:=\:N$ [1]

The total number of boys is: $(N-a)+(N-b) + (N-c)\:=\:3N - a - b - c$

" $\frac{1}{5}$ of all boys are in $B.$"

. . $\frac{1}{5}(3N - a - b - c) \:=\:N - b\quad\Rightarrow\quad 3N - a - b - c\:=\:5N - 5b$

. . . . . . . . . . . . . . $4b\:=\:2N + \underbrace{a + c}_\downarrow$
From [1], we have: . $4b \:=\:2N + N\quad\Rightarrow\quad4b \:=\:3N\quad\Rightarrow\quad b \,=\,\frac{3}{4}N$

Therefore, $\frac{3}{4}$ of class B are girls.