推 koala0416:感謝說明!! 10/10 12:33
※ 引述《koala0416 (koala)》之銘言：
: in a certain game played with red chips and blue chips, each red chip has a
: point value of X and each blue chip has a point value of Y, where X>Y and X
: and Y are positive integers. If a player has 5 red chips and 3 blue chips,
: what is the average (arithmetic mean ) point value of the 8 chips that the
: player has?
: (1) The average point value of one red chip and one blue chip is 5.
: (2) The average point value of the 8 chips that the player has is an integer.
: 此題答案是C還是E呢? 自己覺得是E 因為題目有給出X>Y
: 這樣第二的條件 5X+3Y/8 怎麼配得出整數
: 煩請高手解答
5R:X value
3B:Y value 求(5x+3y)/8
條件(1): x+y = 5*2=10
(2):5x+3y=8n ,n屬於整數
單一條件都不能滿足解答,所以兩條件合併
(2)-(1)*3得: 2x=8n-30
可能的條件為(n,x)=(4,1)(5,5)(6,9)
又 x+y=10 ,x>y 所以只有(6,9)符合
得(x,y)=(9,1) ,(5x+3y)/8=6 ----(C)
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