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求下四海之內的兄弟教我這中四數學題目
發問:
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 .... 顯示更多 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 .
最佳解答:
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
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