Question 550159: A school community had planned to reduce the number of grade 9 students per class room by constructing additional calss rooms. However, they constructed 4 less rooms than they planned. As the result, the number of students per class was 10 more than they planned. If there are 1200 grade 9 students in the school, determine the current number of class rooms and the number of students per class.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A school community had planned to reduce the number of grade 9 students per class room by constructing additional calss rooms. However, they constructed 4 less rooms than they planned. As the result, the number of students per class was 10 more than they planned. If there are 1200 grade 9 students in the school, determine the current number of class rooms and the number of students per class.
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Let "c" be the original number of classrooms.
The 1200/c was the original number of students per classroom.
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Equation:
1200/(c-4) = (1200/c)+10
Multiply thru by c(c-4)
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1200c = 1200(c-4)+10c(c-4)
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1200c = 1200c-4800 + 10c^2-40c
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10c^2-40c-4800 = 0
c^2-4c-480 = 0
Factor:
(c-24)(c+20) = 0
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Positive solution:
c = 24 (# of classrooms originaly planned)
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Cheers,
Stan H.
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