There are a total of 500 students in grades 1 through 5 in an elementary school. 17% of the total number of students are in 1st grade. 19% of the total number of students are in 4th grade. the number of 3rd-grade students is 9 less than the number of 4th-grade students. the number of 2nd-grade student is 10 less than the number of 5th-grade students. how many students are in each grade.

There are 0.17(500) or 85 students in grade 1.

There are 0.19(500) or 95 students in grade 4. 

The number of students in 3rd grade is 95-9 or 86 students.

So, there are a total of 266 students from grade 1,3 and 4. This leaves 234 students for grade 2 and grade 5. 

Let n be the number of students in 5th grade; n-10 is the number of students in 2nd grade. 
     

     

     

There are 122 students in grade 5, and there are 112 students in 2nd grade.