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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
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
At Jefferson Elementary School, the number of teachers and students (k...
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
Number of teachers = (1/17)(510) = 30
Number of students = (16/17)(510) = 480
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
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
Number of 5th and 6th grade students = (1/3)(480 – 96) = (1/3)(384) = 128
Students in first and second grades account for 1/4 of all the students, so:
Number of 1st and 2nd grade students = (1/4)(480) = 120
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
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
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.
Most Upvoted Answer
At Jefferson Elementary School, the number of teachers and students (k...
Let's break down the given information step by step to find the number of students in the third grade compared to the number of students in kindergarten.
Step 1: Total number of students and teachers
The total number of teachers and students at Jefferson Elementary School is 510.
Step 2: Ratio of students to teachers
The ratio of students to teachers is given as 16 to 1. This means for every 16 students, there is 1 teacher.
Step 3: Number of kindergarten students
Kindergarten students make up 1/5 of the student population. Let's assume the total number of students is 16x (since the ratio of students to teachers is 16 to 1). Therefore, the number of kindergarten students is (1/5) * 16x = 16x/5.
Step 4: Number of fifth and sixth graders
Fifth and sixth graders account for 1/3 of the remainder after subtracting kindergarten students from the total. The remainder is (16x - 16x/5) = (80x/5 - 16x/5) = (64x/5). Therefore, the number of fifth and sixth graders is (1/3) * (64x/5) = 64x/15.
Step 5: Number of students in first and second grades
Students in first and second grades account for 1/4 of all the students. Therefore, the number of first and second graders is (1/4) * 16x = 4x.
Step 6: Number of students in third and fourth grades
Since there are an equal number of students in the third and fourth grades, let's assume the number of students in each grade is y. Therefore, the total number of students in the third and fourth grades is 2y.
Step 7: Equating the total number of students to 510
The total number of students can be calculated by adding the number of students in each grade: 16x/5 + 64x/15 + 4x + 2y = 510.
Step 8: Simplifying the equation
To solve the equation, we need to simplify it. Let's find a common denominator to combine the fractions: 3(16x) + x(64x) + 20x + 30y = 2550.
Step 9: Further simplification
By combining like terms, the equation becomes: 48x + 64x^2 + 20x + 30y = 2550.
Step 10: Solving for y
To find the number of students in the third and fourth grades (2y), we need to solve the equation. However, since we are only interested in the difference between the number of students in the third grade and kindergarten, we don't need to find the exact values of x and y.
Step 11: Comparing the number of students in third grade and kindergarten
Since the number of students in the third grade is 2y and the number of students in kindergarten is 16x/5, the difference between them is 2y - 16x/5.
Step 12: Evaluating the difference
Since we don't have the exact values of x and y, we can't find the exact difference. However, we can evaluate the options given and see which one
Step 1: Total number of students and teachers
The total number of teachers and students at Jefferson Elementary School is 510.
Step 2: Ratio of students to teachers
The ratio of students to teachers is given as 16 to 1. This means for every 16 students, there is 1 teacher.
Step 3: Number of kindergarten students
Kindergarten students make up 1/5 of the student population. Let's assume the total number of students is 16x (since the ratio of students to teachers is 16 to 1). Therefore, the number of kindergarten students is (1/5) * 16x = 16x/5.
Step 4: Number of fifth and sixth graders
Fifth and sixth graders account for 1/3 of the remainder after subtracting kindergarten students from the total. The remainder is (16x - 16x/5) = (80x/5 - 16x/5) = (64x/5). Therefore, the number of fifth and sixth graders is (1/3) * (64x/5) = 64x/15.
Step 5: Number of students in first and second grades
Students in first and second grades account for 1/4 of all the students. Therefore, the number of first and second graders is (1/4) * 16x = 4x.
Step 6: Number of students in third and fourth grades
Since there are an equal number of students in the third and fourth grades, let's assume the number of students in each grade is y. Therefore, the total number of students in the third and fourth grades is 2y.
Step 7: Equating the total number of students to 510
The total number of students can be calculated by adding the number of students in each grade: 16x/5 + 64x/15 + 4x + 2y = 510.
Step 8: Simplifying the equation
To solve the equation, we need to simplify it. Let's find a common denominator to combine the fractions: 3(16x) + x(64x) + 20x + 30y = 2550.
Step 9: Further simplification
By combining like terms, the equation becomes: 48x + 64x^2 + 20x + 30y = 2550.
Step 10: Solving for y
To find the number of students in the third and fourth grades (2y), we need to solve the equation. However, since we are only interested in the difference between the number of students in the third grade and kindergarten, we don't need to find the exact values of x and y.
Step 11: Comparing the number of students in third grade and kindergarten
Since the number of students in the third grade is 2y and the number of students in kindergarten is 16x/5, the difference between them is 2y - 16x/5.
Step 12: Evaluating the difference
Since we don't have the exact values of x and y, we can't find the exact difference. However, we can evaluate the options given and see which one
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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 greaterb)17 fewerc)28 fewerd)36 fewere)44 fewerCorrect answer is option 'C'. Can you explain this answer?
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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 greaterb)17 fewerc)28 fewerd)36 fewere)44 fewerCorrect answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about 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 greaterb)17 fewerc)28 fewerd)36 fewere)44 fewerCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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 greaterb)17 fewerc)28 fewerd)36 fewere)44 fewerCorrect answer is option 'C'. Can you explain this answer?.
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 greaterb)17 fewerc)28 fewerd)36 fewere)44 fewerCorrect answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about 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 greaterb)17 fewerc)28 fewerd)36 fewere)44 fewerCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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 greaterb)17 fewerc)28 fewerd)36 fewere)44 fewerCorrect answer is option 'C'. Can you explain this answer?.
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