數學方程........唔識

我的答案都是12隻, 不過同樓上計法有別....
我是用聯立二元一次方程式 (simultaneous linear equation)

設x = 原有杯的數目, y = 原有杯的價錢

打爛杯前: xy = 48 (1式)

打爛杯後: (x - 2) (y + 3) = 48 + 22
(x - 2) (y + 3) = 70 (2式)

1式: y = 48/x (3式)

把3式代入2式: (x - 2) (48/x + 3) = 70
48 + 3x - 96/x - 6 = 70
3x - 96/x - 28 = 0
3x^2 - 96 - 28x = 0
(x - 12) (3x + 8) = 0
x = 12 or -8/3 (捨去rejected)

答案: 原有杯12隻, 成本$4一隻 == 成本 $48
後來, 爛兩隻杯, 得10隻;
售價比成本高$3, 即售價$7一隻
全部賣出 == $70
利潤 = 售價 - 成本
= $70 - $48
= $22

設買入玻璃杯x隻
{ (48/x) + 3 }(x-2) = 48 + 22
(48x - 96)/x +3x - 6 = 70
(48x - 96)/x +3x = 76
48 - 96/x + 3x = 76
48x - 96 +3x^2 = 76x
x^2-x - 96 = 0
(3x + 8 ) (x - 12 ) = 0
x = 12 or x = -8/3 (rejected)
所以原有玻璃杯12隻


2006-11-18 14:41:06 補充：
x^2-x - 96 = 0 >> 不好意思, 這行打錯了, 應該是 3x^2 - 28x - 96 = 0

let x be the no.of the glass
(x-2)(48/x+3)-48=70
3x^2-28x-96=0
(x-12)(3x+8)=0
x=12 or -8/3(rejected)
Thus, x=12

check your question, no solution if the answer is an integer.

(i dun really think anyone can sell u 41.333 glasses ..)

收入-成本=利潤
(51(x-2))-(48x)=22
51x-102-48x=22
3x=124
x=41 1/3

(48 / X +3)(X - 2) = 48 + 22

48-(48-48/yx2)=22