let

b1 = the number of boys in the first class

g1 = the number of girls in the first class

b2 = the number of boys in the second class

g2 = the number of girls in the second class

both classes have the same number of students

b1 + g1 = b2 + g2

The ratio of boys to girls in one class is 2 to 3,

b1/g1 = 2/3

b1 = (2/3)g1

and in the other class it is 4 to 3

b2/g2 = 4/3

b2 = (4/3)g2

What is the ratio of boys to girls in the whole seventh grade?

(b1 + b2)/(g1 + g2) = ((2/3)g1 + (4/3)g2)/(g1 + g2) = (2/3)(g1 + 2g2)/(g1 + g2) = (2/3)(1 + g2/(g1 + g2))

we can also use the fact that b1 + g1 = b2 + g2 and plug b1 = (2/3)g1 and b2 = (4/3)g2 into it

(2/3)g1 + g1 = (4/3)g2 + g2

g1(5/3) = g2(7/3)

g1 = g2(7/3)(3/5)

g1 = (7/5)g2

now we have

(b1 + b2)/(g1 + g2) = (2/3)(1 + g2/(g1 + g2)) = (2/3)(1 + g2/((7/5)g2 + g2)) = (2/3)(1 + 1/((7/5) + 1)) = 17/18

the ratio of boys to girls in the whole seventh grade is 17:18.

How many total students are in the seventh grade?

b1 + b2 + g1 + g2 = 2(b1 + g1) = 2((2/3)g1 + g1) = 2g1(2/3 + 1) = 2g1*(5/3) = (10/3)g1

we have 4 unknowns: b1, b2 ,g1 and g2 and 3 conditions thus there are infinitely many solutions.

for example one solution will be for g1 = 21 girls in the first class

b1 = (2/3)*21 = 14 boys

g2 = (5/7)g1 = (5/7)*21 = 15 girls

b2 = (4/3)g2 = (4/3)*15 = 20 boys

indeed

21 + 14 = 15 + 20

14:21 = 2 : 3

20 : 15 = 4 : 3

in this case the total number of students in the seventh grade will be 2*35 = 70 students.