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

Question

Pablo Carson

Mathematics

4 December, 00:10

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

+5

Answers (1)

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Curry · Answer 1

Answer: option D is the correct answer.

Step-by-step explanation:

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.

The dollar per student ratio for the high school is r/300

The dollar per student ratio for the middle school is r/200

Later, the middle school transferred s dollars to the high school so that they would have received the same funding per student.

The dollar per student ratio for the high school would be (r + s) / 300

The dollar per student ratio for the middle school would be (r - s) / 200

Since both rates are the same, then

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

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

300r - 300s = 200r + 200s

200s + 300s = 300r - 200r

500s = 100r

s = 100r/500

s = r/5