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

Question

Mathematics

Chucky

20 January, 16:08

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

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Answers (1)

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Matthias Snow · Answer 1

C. 28 fewer

Step-by-step explanation: Total population of students and teachers = 510

Students : teacher = 16 : 1

Population of students = 16/17 * 510 = 480 students

Number of kindergarten students = 1/5 of 480 = 1/5*480 = 96

Number of grade 5 and 6 students = 1/3 of (480 - 96) = 1/3*384 = 128

Number of grade 1 and 2 students = 1/4 of 480 = 1/4*480 = 120

Number of grade 3 and 4 = 480 - (96+128+120) = 480 - 344 = 136

Number of grade 3 students = 136/2 = 68

Number of kindergarten students = 96

Therefore, the number of students in grade 3 is 28 (96 - 68 = 28) fewer than the number of students in kindergarten