Question

英语应用题一题(需要解题步骤)

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 of 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 your work.

Answer 1

先翻成中文吧这样就容易明白多了
A 班和B班所有的学生人数相同，A班的男孩和女孩的人数比例是3比2，B班的男孩是女孩人数的200%。如果让A班的一个女孩和B班的一个男孩换班，那么A，B两班的男孩和女孩的人数比例就相等，求两班的男孩和女孩的人数
设A班男生人数为X，那么A班女生人数是（2/3）X
再设B班男生人数为Y，那么B班女生人数是 Y/2，可得出方程组
X+（2/3）X=Y+ Y/2
（X+1）：[（2/3）X-1]=（Y-1）：（Y/2+1）
由方程1得出 （5/3）X=（3/2）Y，10X=9Y，X=（9/10）Y
代入方程2得出 [(9/10)Y+1]：[(2/3)*(9/10)Y-1]=(Y-1):(Y/2+1)
解方程得 Y=20 或Y=0，由于Y=0没意义，所以B班男生人数是20
则B班女生人数是20/2=10
A班男生人数是 （9/10）Y=18，A班女生人数是（2/3）*18=12
终上所述，A班男生人数是18人，女生人数是12人
B班男生人数是20人，女生人数是10人

Answer 2

我帮你把方程列出来吧：
有四个未知数，x1, A班男生 x2,A班女生 x3, B班男生 x4， B班女生
x1 + x2 = x3 + x4
x1 : x2 = 3:4
x3 = x4 * 200%
(x1+1): (x2-1) = (x3-1) : (x4+1)

Answer 3

There are 30 students in each class. 3:2 and 2:1 We can know the number students of each class should be at least 15 persons. and if they switch a boy and a girl, the ratios will be the same We can know boys in class B should be two more than in Class A. 15X2=30. so the boys in class A should be 18 persons. The boys in Class B should be 20 persons.

Answer 4

Assume there are 2x girls in Class A, and there are 3x boys in Class A. Assume there are y girls in class B, and there are 2y girls in Class B. According to the discription, we have an equation: 2x-1/3x 1=y 1/2y-1
And we have: 5x=3y
And x=6, y=10.
So there are 18boys and 12girls in Class A.
And 20 boys and 10 girls in Class B

Answer 5

和GMAT的数学题很相似