大院里养了三种动物。每只小山羊戴3个铃铛,每只狗戴1个铃铛

  • 时间:2020-04-24 15:44:06
  • 分类:数学世界
  • 阅读:171 次

大院里养了三种动物。每只小山羊戴3个铃铛,每只狗戴1个铃铛,大白鹅不戴铃铛。小明数了数,一共有9个脑袋,28条腿,11个铃铛。问三种动物各几只?

解答:

题目很复杂,不同于一般的鸡兔同笼问题。但可以化难为易。比如:小山羊和狗都是四条腿的,属于同类,先不考虑戴铃铛的情况。

假设全是鹅,共有腿数:9×2=18(条)

与实际的相差:28-18=10(条)

10÷(4-2)=5(只)…………狗和山羊的总只数

鹅的只数:9-5=4(只)

再利用铃铛的情况来计算狗和山羊的只数:

假设5只全是狗:5×1=5(个)

11-5=6(个)

6÷(3-1)=3(只)………………山羊

狗:5-3=2(只)

答:鹅4只,狗2只,山羊3只。

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