訂購 Herman Yeung 數學天書詳情

2016年7月4日 星期一

鈺成其事 之 迷戀數學 之 計數果 part



https://tsangyoksing.hk/2016/07/04/%E8%BF%B7%E6%88%80%E6%95%B8%E5%AD%B8/


Question 1:
設 x 隻山雞、y 隻黃狼、z 隻九頭鳥
頭 = x + y + 9z = 100............(1)
腳 = 2x + 4y + 2z = 100.......(2)
(2)  (1)*2
2y  16z = -100
Let z = t, y = 8t – 50
Put into (1)
x + (8t  50) + 9t = 100
x = 150  17t
Solution Set 解集
={(150 17t, 8t  50, t): t belongs to real}
但 x, y, z 係正整數
150  17t > 0,  t < 8.82
8t  50 > 0, t > 6.25
而 t 為整數
t = 7 or 8
When t = 7  (x, y, z) = (31, 6, 7)
When t = 8  (x, y, z) = (14, 14, 8)

Question 2:
設 x 隻山雞、y 隻黃狼、z 隻九頭鳥
頭 = 2x + 2y + 10z = 100............(1)
腳 = 3x + 5y + 3z = 100.......(2)
(1)*3 - (2)*2
4y + 24z = 100
Let z = t, y = 6t  25
Put into (1)
2x + 2(6t  25) + 10t = 100
x = 75  11t
Solution Set 解集
={(75  11t, 6t - 25, t): t belongs to real}
但 x, y, z 係正整數
75  11t > 0,  t < 6.82
6t  25 > 0, t > 4.17
而 t 為整數
t = 5 or 6
When t = 5  (x, y, z) = (20, 5, 5)  Total = 30
When t = 6  (x, y, z) = (9, 11, 6)  Total = 26


Herman Yeung


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2 則留言:

Aa Lau 提到...

Herman, (2)-(1)*2
點解要乘2?

Herman Yeung 提到...

為左消左 X 的變數