一道英文数学难题!火速回答!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
2019-06-14
一道英文数学难题!火速回答!
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.
希望过程可以短一点
注意是两班！
不是只要一班的！
优质解答
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.
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.