標題:
一條F.1數學
發問:
農場內有一些雞和兔 三分之一的兔子只得三隻腳... 若雞和兔共有35個頭和90隻腳.. 求雞和四腳兔(即正常兔)分別有多少隻
最佳解答:
Let X = 雞 Let Y = 兔 X + Y = 35 (一共有35隻) 2X + ((2/3 Y) x 4) + ((1/3 Y) x 3) = 90 (兩隻腳的雞 + 4隻腳的正常兔 + 3隻腳的不正常兔 共有90隻腳) (70 - 2Y) + 8Y/3 + 3Y/3 = 90 (210 - 6Y)/3 + 8Y/3 + 3Y/3 = 90 210 - 6Y + 8Y + 3Y = 270 5Y = 60 Y=12 所以 X = 23 (雞) 正常兔 = 12 x 2/3 = 8 (正常兔)
其他解答:
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let x be no. of chicken y be no. of 4-leg rabbits z be no, of 3-leg rabbits x+y+z = 35 (1) 2x+4y+3z = 90 (2) z = (y+z) / 3 (3) from (3) z = y/3 + z/3 2z/3 = y/3 z = y/2 put z = y/2 into (1) x+y+y/2 = 35 x+3y/2 = 35 x = 35-3y/2 put x = 35-3y/2 into (2) 2(35-3y/2)+4y+3(y/2) = 90 70-3y+4y+3y/2 = 90 2.5y = 20 y = 8 z = 4 x = 23 雞 : 23 四腳兔 : 8
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