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In a local school district, the high school and middle schoo

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In a local school district, the high school and middle schoo

by BTGmoderatorDC » Sun Sep 22, 2019 8:08 pm

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In a local school district, the high school and middle school each received r dollars toward funding for the student arts program. The high school enrolled 300 students and the middle school enrolled 200 students. Later, the middle school transferred s dollars to the high school so that they would have received the same funding per student. Which of the following is equivalent to s?

A. r/2
B. r/3
C. r/4
D. r/5
E. r/6

OA D

Source: Manhattan Prep
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by Jay@ManhattanReview » Sun Sep 22, 2019 11:01 pm
BTGmoderatorDC wrote:In a local school district, the high school and middle school each received r dollars toward funding for the student arts program. The high school enrolled 300 students and the middle school enrolled 200 students. Later, the middle school transferred s dollars to the high school so that they would have received the same funding per student. Which of the following is equivalent to s?

A. r/2
B. r/3
C. r/4
D. r/5
E. r/6

OA D

Source: Manhattan Prep
Funds with the middle school after transfer of $s = $(r - s);
Funds with the high school after transfer of $s = $(r + s);

Funding per student with the middle school after transfer of $s = $(r - s)/200;
Funding per student with the high school after transfer of $s = $(r + s)/300;

Thus, we have (r - s)/200 = (r + s)/300

=> s = r/5

The correct answer: D

Hope this helps!

-Jay
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by Scott@TargetTestPrep » Tue Sep 24, 2019 2:32 pm
BTGmoderatorDC wrote:In a local school district, the high school and middle school each received r dollars toward funding for the student arts program. The high school enrolled 300 students and the middle school enrolled 200 students. Later, the middle school transferred s dollars to the high school so that they would have received the same funding per student. Which of the following is equivalent to s?

A. r/2
B. r/3
C. r/4
D. r/5
E. r/6

OA D

Source: Manhattan Prep
After the transfer, the middle school has (r - s) and the high school has (r + s) dollars. The funding per student for the middle school and the high school are (r - s)/200 and (r + s)/300, respectively. Since we are told that the funding per student is the same for both schools, we have:

(r - s)/200 = (r + s)/300

300r - 300s = 200r + 200s

100r = 500s

r = 5s

s = r/5

Answer: D

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