At the beginning of grade 6 the number of advanced math to the number of regluar math students was 3: 8 however after taking placement tests students were moved around chaning the ratio of the number of advanced math students to the number of regluar math students was 4: 7 how many student students started in reglaur math and advanced math if there were 92 students in advanced math after the placement test

The number of students would not change between before the test and after the test. 3+8 and 4+7 both = 11 so finding out how many students would equal one ratio can then be used to find how many equal 3 and 8. 

If 92 students are equal to 4 in the ratio, then 1 in the ratio is worth 23 students. This is important as then when you times 23 by 7 you find out how many students there are in the regular maths class, 161 students. Plussing these two together gives you a total of 253 students.

Using this 253 you can divide it by 11 to find out how much 1 number would be in the ratio, it equals 23. Using this you can then times 23 by both 3 and 8 to find the original class sizes, 3x23 = 69, and 23x8 = 184.

Making the origional class size of the advaced class 69 studnets, and the regular maths class size 184.