九头鸟问题

  • 时间:2020-04-03 19:50:42
  • 分类:数学世界
  • 阅读:146 次

传说,九头鸟有九头一尾,九尾鸟有九尾一头。今两种鸟共有头52个、尾68条。这两种鸟各有多少只?

此题本质上仍属于“鸡兔同笼”问题,但解法时如用假设法,理解起来有一定的难度,所以可尝试方程解法。

解题思路:利用关系式“九头鸟的尾巴数+九尾鸟的尾巴数=68”来列方程。

解答过程如下:

解:设九头鸟有x只,则九尾鸟的只数可用(52-9x)来表示(此处理解起来有一定的难度,一定要想明白)。

1×x+(52-9x)×9=68

解此方程,得x=5,即九头鸟有5只,九尾鸟有52-9×5=7(只)。

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