Question

一道英文数学难题！！火速回答！！急！！！

Class A and class B have the same number of students.In class A,the ratio of boys to girls is 3 to 2. In class B,the number fo boys is 200% of the number of girls.If one girl in class A and one boy in class b switch classes,the ratios of boys to girls in both classes will be the same.Find the numbers of boys and girls in the two classes.Show all you work.
怎么做这道题呀！！
我不会！！
希望过程可以短一点
拜托了
起码易懂一点！！！！~~~~~
注意是两班！！！
不是只要一班的！！！！

Answer 1

A班和B班具有相同数量的学生数.在 A班的男孩女孩比例相同数量是3比2。在B班，男生人数是女生的2倍，如果一个女生在A班 和 一个在B班的男生 交换班 那么男女比率将相同 在这2个班上将是相同的 算出2个板上男女生 的 人数

Answer 2

Suppose the numbers of boys and girls of class A are 3X and 2X respectively, and the numbers of boys and girls of class B are 2Y and Y respectively.
Then we get:
3X+2X=2Y+Y
(3X+1)/(2X-1)=(2Y-1)/(Y+1)
把这两个方程解出来，可以得到：X=6,Y=10

Answer 3

Let the number of girls in class A be X.
Let the number of boys in class B be Y.

Initially, X / Y = 3 / 2
Y = 3X/ 2

Let the number of girls in class B be x.
Let the number of girl in class B be y.
Initially, y / x = 2
y = 2x

X + Y = x + y
X + 3X/2 = x + 2x
5/2 X = 3 x

After one girl in class A is replaced by one boy in class B
(X - 1) / (Y + 1) = (x + 1) / (y - 1) --> multiple both side by (Y + 1)(y - 1)
(X - 1)(y - 1) = (x + 1) (Y + 1)
Express y and Y in terms of X
(X - 1)(2x - 1) = (x + 1) (3X/2 + 1)
2Xx - X - 2x + 1 = 3/2 * Xx + x + 3/2 * X + 1
1/2 * Xx - 5/2 X - 3x = 0
Since 5/2 X = 3 x
1/2 * Xx - 3x - 3x = 0
Xx - 6x = 0
Since X = 6x/5
6x/5 * x - 6x = 0
6x*x - 30x = 0
x (6x - 30) = 0
x = 0 OR 6x = 30
x = 5

y = 2x y = 10

X = 6x/5 = 6

Y = 3X/ 2 = 9

过程绝对不应该这么复杂 >.< 不过答案似乎正确.