Question

At Jefferson Elementary School, the number of teachers and students (kindergarten through sixth grade) totals 510. The ratio of students to teachers is 16 to 1. Kindergarten students make up 1/5 of the student population and fifth and sixth graders account for 1/3 of the remainder. Students in first and second grades account for 1/4 of all the students. If there are an equal number of students in the third and fourth grades, then the number of students in third grade is how many greater or fewer than the number of students in kindergarten?

A. 12 greater
B. 17 fewer
C. 28 fewer
D. 36 fewer
E. 44 fewer

Answer 1

Option C.

Explanation:

The number of teachers and students (kindergarten through sixth grade) totals is 510.

The ratio of students to teachers is 16:1.

16+1=17

Total number of students =
`510* (16)/(17)=480`

Kindergarten students make up 1/5 of the student population and fifth and sixth graders account for 1/3 of the remainder.

Kindergarten students =
`480* (1)/(5)=96`

5th-6th grade students =
`(480-96)* (1)/(3)=384* (1)/(3)=128`

Students in first and second grades account for 1/4 of all the students.

1st-2nd grade students =
`480* (1)/(4)=120`

An equal number of students in the third and fourth grades.

Let x be the number of students in class third.

3rd-4th grade students =
`x+x=2x`

Total students = Kindergarten + (1st-2nd) + (3rd-4th) + (5th-6th)

`480=96+120+2x+128`

`480=344+2x`

`480-344=2x`

`136=2x`

Divide both sides by 2.

`68=x`

It means number of students in grade 3 is 68.

`68-96=-28`

It means in third grade 28 fewer students than the number of students in kindergarten.

Therefore, the correct option is C.