Hi there-
Below is a 600-700 level question I missed during a practice test. I reviewed the solution provided and understand it. However, it seems impossible to work through all the algebra shown in the solution in less than 2 mins. Does anyone have any suggestions on a faster way to approach this? Or is there no way around all the time consuming algebra?
thanks!
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?
12 greater
17 fewer
28 fewer
36 fewer
44 fewer
Answer = 28 fewer
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AndreaV424
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First, we want to figure out the total number of students. We know the ratio of students to teachers is 16:1.
16/1 = S/T
T16= S
And we know S + T = 510.
Plug in T16 for S in the above equation:
T16 + T = 510 which equals 17T = 510. So we find T = 30. Now we know there are 30 teachers and if (S= T16) then there are 480 student (16 * 30).
Total # of students is 480.
Kindergarten is 1/5 of 480 = 96 kindergarteners
5th AND 6th graders is 1/3 of the remaining. The remaining # is 384. (480-96 = 384). 1/3 of 384 = 128
1st & 2nd grader is 1/4 of all students (480) so that equals 120.
add your totals up to get the remaining..
Kindergaten 96
1st and 2nd 120
3and 4th ?
5th and 6th 128
Total 344
480- 344 = 136 (these will be between 3rd and 4th graders) and the problem states that 3rd and 4th graders are equal. 136/2 = 68 students each
Answer the final question. There are 68 3rd graders and 96 kindergarteners. The difference is 28. There are 28 fewer 3rd fraders than there are kindergarteners.
I hope this helps. Please feel free to message me with any questions.
16/1 = S/T
T16= S
And we know S + T = 510.
Plug in T16 for S in the above equation:
T16 + T = 510 which equals 17T = 510. So we find T = 30. Now we know there are 30 teachers and if (S= T16) then there are 480 student (16 * 30).
Total # of students is 480.
Kindergarten is 1/5 of 480 = 96 kindergarteners
5th AND 6th graders is 1/3 of the remaining. The remaining # is 384. (480-96 = 384). 1/3 of 384 = 128
1st & 2nd grader is 1/4 of all students (480) so that equals 120.
add your totals up to get the remaining..
Kindergaten 96
1st and 2nd 120
3and 4th ?
5th and 6th 128
Total 344
480- 344 = 136 (these will be between 3rd and 4th graders) and the problem states that 3rd and 4th graders are equal. 136/2 = 68 students each
Answer the final question. There are 68 3rd graders and 96 kindergarteners. The difference is 28. There are 28 fewer 3rd fraders than there are kindergarteners.
I hope this helps. Please feel free to message me with any questions.
