From 621b259fb93f112a3cb4235cfc3bc97dfa8bbc06 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E8=B5=B5=E9=91=AB?= <7176466@qq.com> Date: Fri, 12 Aug 2022 20:03:08 +0800 Subject: [PATCH] =?UTF-8?q?=E6=B7=BB=E5=8A=A0=E5=9B=BE=E7=89=87?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 问题/鸡兔同笼.md | 26 ++++++++++++++++++++------ 问题/鸡兔同笼.png | Bin 0 -> 467414 bytes 2 files changed, 20 insertions(+), 6 deletions(-) create mode 100644 问题/鸡兔同笼.png diff --git a/问题/鸡兔同笼.md b/问题/鸡兔同笼.md index 53c5ceb..568b3a9 100644 --- a/问题/鸡兔同笼.md +++ b/问题/鸡兔同笼.md @@ -22,14 +22,28 @@ ### 假设法 -35头说明鸡和兔共35只,假设35只全为鸡,则应有(35×2)=70只足,实则94只足,还差94-70=24只足,兔子4只足,鸡2只足,一只鸡换成一只兔子可以补上2只足,现需补上24只足,也就是需鸡换兔24÷2=12只,只数不变,足补齐94只,即兔子12只,鸡23只,实际上这其实是二元一次联立方程式用消元求法求x的方法. - -### 举手法 - -按[李永乐老师讲解的鸡兔同笼问题的视频](https://youtu.be/tnKaBeDVFLU)中的解法思路:鸡和兔子的足共有94只,如果让所有的动物都举起手来(抬起两只足,鸭子只能坐在地上了),则35只动物共抬起了$2 \times 35 = 70$只足,在地上还剩$94-70=24$只足。因为这些足全是双足站立的兔子们的,所以兔子的数量是$24 \div 2=12$只。 +35头说明鸡和兔共35只,假设35只全为鸡,则应有$2 \times 35 =70$只足,实则94只足,还差$94-70=24$只足,兔子4只足,鸡2只足,一只鸡换成一只兔子可以补上2只足,现需补上24只足,也就是需鸡换兔$24 \div 2=12$只,只数不变,足补齐94只,即兔子12只,鸡23只,实际上这其实是二元一次联立方程式用消元求法求x的代数方法(下一个方法)。 ### 代数法 解: 设鸡有$x$只, 兔有$y$只,则: -$ \begin{cases}x+y=35\\ 2x+4y=94\end{cases} $ +$ \begin{cases}\begin{aligned}x+y=35\\ 2x+4y=94\end{aligned}\end{cases}$ + +$ x = 35-y $ + +$ (35-y) \times 2 + 4y = 94 $ + +$ 2y = 24 $ + +$ y = 12$ + +$ x = 35 - y = 23$ + +答: 有鸡23只,有兔12只。 + +### 抬脚法 + +按[李永乐老师讲解的鸡兔同笼问题的视频](https://youtu.be/tnKaBeDVFLU)中的解法思路:鸡和兔子的足共有94只,如果让所有的动物都举起手来(抬起两只足,鸭子只能坐在地上了),则35只动物共抬起了$2 \times 35 = 70$只足,在地上还剩$94-70=24$只足。因为这些足全是双足站立的兔子们的,所以兔子的数量是$24 \div 2=12$只。 + +![](鸡兔同笼.png) diff --git a/问题/鸡兔同笼.png b/问题/鸡兔同笼.png new file mode 100644 index 0000000000000000000000000000000000000000..5f6ffd869e9098b08738e31588b43fff15729161 GIT binary patch literal 467414 zcmeFYV|yi0w>2Ewc6O{C+qOFCPO@X$9oz2M?$}1hwr!_7ww)*Uea`t0?}zu>s;YI( zs#-P2ni!)Zz9~r~BM=~ffq@~*%1Ee!fkA-4z@W(CV7|_{p$3V9fdRl|B}9L?XPsrc 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