I am a grade 12 math student who would like to know if there is an easy way to solve

In a school the ratio of the number of Grade 11 students to the number of grade 12 students is 4:3. If there were 5 fewer students in grade 11 and 3 more students in grade 12, the ratio would be 7:6. How many students in each grade?

Sincerly,
Jennifer

Suppose that the number of Grade 11 students is x and the number of Grade 12 students is y then the first statement says that the ratio x:y is 4:3, that is

x/y = 4/3.

The second statement says that if the number of Grade 11 students is 5 fewer, that is x-5, and the number of Grade 12 students is 3 more, that is y+3, then the ratio is 7:6. Thus

(x-5)/(y+3) = 7/6.

Now you have two equations in x and y which you can solve.

Cheers,
Penny