[問題]考古題 PS Form 17sec08-Q14

[eiswein]

The King School has an enrollment of 900 students. The school day at King consists of 6 class periods, each of which is taught by one teacher, and there is an average of 30 students per class. If each teacher at King teaches 5 of the 6 periods and has one period free, but no student has a free period, how many teachers does the school have?

(A) 25
(B) 30
(C) 36
(D) 60
(E) 150



答案是(C)
這題題目我好像沒有完全看懂
算出來的答案沒有在答案選項裡..

可以請教會算的人幫忙解釋嗎?
THX~

[simonyu]

題目大概是說學校有900名學生，平均每班30人，而每班學生都要上6個學期，但老師只需要教5個學期即可，問有多少老師執教？

因為題目沒有要求極端值，所以以平均值來算的話，
900/30=30班
因為每班學生要上六學期，一個老師卻教五學期，會有一學期空著，
假設讓各班缺老師的學期錯開來，排列如下:
a班:空-有-有-有-有-有
b班:有-空-有-有-有-有
c班:有-有-空-有-有-有
d班:有-有-有-空-有-有
e班:有-有-有-有-空-有
.......

也就是說，只要照這樣安排，每五班只要再多安排一個老師即可，是比較經濟的做法，所以原本每班一個+需要多安排的老師=
30+30/5=36

答案C

[eiswein]

感謝熱心的simonyu