Question

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.

Answer 1

122 students in 5th grade, 112 in second grade

Answer 2

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.

`n+\left(n-10\right)=234`


`2n=244`


`n=122`

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