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

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

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In a local school distirct, 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

The OA is D.

I'm really confused with this PS question. Experts, any suggestion? Why D is the correct answer? Thanks in advance.

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LUANDATO wrote:
In a local school distirct, 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
Since each student must have the same funding, let the funding per student = $1.

Since the high school has 300 students, the amount required by the high school = 300*1 = $300.
Since the middle school has 200 students, the amount required by the middle school = 200*1 = $200.
Total amount distributed to the two schools = 300+200 = $500.
Since each school originally received r dollars, and the total amount distributed was $500, r = $250.
Since the middle school originally had $250 and gave away s dollars to end with only $200, s = $50.

The question stem asks for the value of s (50). This is the target value.
Now plug r=250 into the answers to see which yields the target value of 50.
Only D works:
r/5 = 250/5 = 50.

The correct answer is D.

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LUANDATO wrote:
In a local school distirct, 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

The OA is D.

I'm really confused with this PS question. Experts, any suggestion? Why D is the correct answer? Thanks in advance.
Alternatively, you can say that each school receives $600 to start. (So r = 600.)
If the middle school gives the high school s dollars, the middles school will have 600 -s dollar sand the high school will have 600 + s dollars.

Average funding for middle school. = (600 -s)/200
Average funding for high school. = (600 + s)/300

These values should be equal. (600 -s)/200 = (600 + s)/300
Multiply both sides by 600 to get 3(600-s) = 2(600 +s)
1800 -3s = 1200 + 2s
600 = 5s
s = 120.

When we plug in '600' for 'r,' the correct answer will yield 120, our target.
Only D works. 600/5 = 120.

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LUANDATO wrote:
In a local school distirct, 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

The OA is D.

I'm really confused with this PS question. Experts, any suggestion? Why D is the correct answer? Thanks in advance.
If the high school received r dollars, and it has 300 students, then the funding per student would be r/300

If the middle school received r dollars, and it has 200 students, then the funding per student would be r/200.

If the middle school transfers s dollars to the high school, the total funding of the high school would be r + s, and the funding per student would be (r + s)/300
Similarly the middle school would have total funding of r -s and funding per student of (r-s)/200
We know those two values are equal so (r+s)/300 = (r-s)/200
Multiply both sides by '600' to get 2(r+s) = 3(r-s).

(Note: 600 is a nice number to use as it's a multiple of both 300 and 200. 600/300 = 2 and 600/200 = 3.)

2r + 2s = 3r -3s
5s = r
s = r/5. The answer is D

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For each dollar a student gets, then collectively the schools get $500 split equally between them = $250 per school.
Transferring $50 will create $200 and $300 as required.
$250 / $50 = 5
Therefore, $ = r/5

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