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一題方程式題目
Sep 22nd 2013, 13:19

設瓶蓋容量為x單位,整瓶是y單位

所以誤看而使用的5n次中,共用去了5n.x/2 = 5nx/2

此時發現用錯了,而剩下的是(n-1)/n,也就是用去了1/n
所以用去的 5nx/2 : y = 1 : n

=>y = 5xn^2/2
=>2y = 5xn^2

此時剩下 y - 5nx/2,還可以用21n+6次,(這時改回來用正確的用量,每次x/3)
表示 (y - 5nx/2) ÷ x/3 = 21n+6

=> y - 5nx/2 = (21n+6).x/3 = 7nx + 2x
=> 2y - 5nx = 14nx + 4x
 
2y = 5xn^2代入上式
=>
5xn^2 - 5nx = 14nx + 4x
=>
5xn^2 - 19nx - 4x = 0
5n^2 - 19n - 4 = 0
(5n + 1)(n - 4) = 0
n = 4 (負不合)
 
因為2y = 5xn^2
=>y/x = 5n^2/2 = 5.4^2/2 = 5.16/2 = 40

 

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