求下四海之內的兄弟教我這中四數學題目

alan007566

2009-03-19 1:08 am

A shepherd is herding his sheep on a piece of grassland . If he herds
50 sheep , all grass will be eaten after 38 weeks ; if he herds 80
sheep , all grass will be eaten after 8 weeks . Given that the amount
of grass eaten by every sheep is the same every day and that the
grass grows with a constant rate . If he hopes that the grass will not
be eaten up forever , what is the maximum number of sheep he can
herd ?

Please set up simultaneous linear equation in two unknowns to solve
the problem .

回答 (1)

用戶2053

2009-03-19 2:07 am

✔ 最佳答案

設原有草量A ,草每週生長量B 設每只羊每週吃草量是C :
原有草 + 吃完所需週數所生長草量 = 羊數 *每只羊每週吃草量 *週數
A + 38B = 50C * 38 ...(1)
A + 8B = 80C * 8 ...(2)
(1)、(2)兩邊除以C :
A/C + 38B/C = 1900...(3)
A/C + 8B/C = 640...(4)
(3)-(4):
30B/C = 1260
B/C = 42,代回(4)
A/C = 640 - 8 * 42 = 304
所以 A : B = 304 : 42 , B : C = 42 : 1
A : B : C = 304 : 42 : 1
要羊永遠吃不完草 :
則羊數 * 每只羊每週食草量 <= 草的每週生長量
羊數 * C <= B
羊數 <= (B / C = 42)
So he can maximum herd 42 sheeps that the grass will not
be eaten up forever.

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