crejoc wrote:
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
Official Explanation:
We know that the student to teacher ratio at the school is 16 to 1, and the total number of people is 510.
Therefore: Number of students = (16/17)(510) = 480 and Number of teachers = (1/17)(510) = 30
Kindergarten students make up 1/5 of the student population, so: Number of kindergarten students = (1/5)(480) = 96
Fifth and sixth graders account for 1/3 of the remainder (after kindergarten students are subtracted from the total),
therefore: Number of 5th and 6th grade students = (1/3)(480 – 96) = (1/3)(384) = 128 Students
first and second grades account for 1/4 of all the students,
so: Number of 1st and 2nd grade students = (1/4)(480) = 120
So far, we have accounted for every grade but the 3rd and 4th grades, so they must consist of the students left over:
Number of 3rd and 4th grade students = Total students – students in other grades
Number of 3rd and 4th grade students = 480 – 96 – 128 – 120 = 136
If there are an equal number of students in the third and fourth grades, then: Number of 3rd grade students = 136/2 = 68
The number of students in third grade is 68, which is fewer than 96, the number of students in kindergarten.
The number of students in 3rd grade is thus 96 – 68 = 28 fewer than the number of kindergarten students.
The correct answer is C.