POW #5:A Cycling Problem
POW #5:A Cycling Problem
Orville and Wilbur owned a bicycle shop which also sold tricycles.One day,they decided to take an inventory of their stock.They each volunteered to count one item,which would have worked out just fine if one had counted bicycles and the other had counted tricycles.But,Orville and Wilbur were very independent thinkers.Orville counted the number of pedals in the shop and Wilbur counted the number of wheels.
Orville found that they had 144 pedals in the shop,and Wilbur found that they had 186 wheels.All pedals and wheels were actually parts of either bicycles or tricycles.They were just about to start over with their inventory when their friend,Kitty Hawkins,who was a good problem-solver,challenged them to figure out the number of bicycles and tricycles from the inventory they had already done.
Can you help the Wright brothers?
Orville and Wilbur owned a bicycle shop which also sold tricycles.One day,they decided to take an inventory of their stock.They each volunteered to count one item,which would have worked out just fine if one had counted bicycles and the other had counted tricycles.But,Orville and Wilbur were very independent thinkers.Orville counted the number of pedals in the shop and Wilbur counted the number of wheels.
Orville found that they had 144 pedals in the shop,and Wilbur found that they had 186 wheels.All pedals and wheels were actually parts of either bicycles or tricycles.They were just about to start over with their inventory when their friend,Kitty Hawkins,who was a good problem-solver,challenged them to figure out the number of bicycles and tricycles from the inventory they had already done.
Can you help the Wright brothers?
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这是一道典型的“鸡兔同笼”问题.
分析：每辆自行车有2个轮子,每辆三轮车有3个轮子.
一、用算术
先确定有多少辆车因为不管自行车还是三轮车每辆车的踏板都是2个,所以三轮车和自行车一共有：
144÷2=72(辆)
假设法：
假设全是自行车那么轮子数：2×72＝144(只) 比总的轮子数少：186－144＝42(只)
三轮车：42÷（3-2）＝42(辆)
自行车：72－42＝30(辆)
二、用方程
设三轮车有x辆,则自行车有72-x辆.
3x+2(72-x)=186
x=186-144 =42（辆）
自行车：
72-42=30（辆）
答：三轮车有42只,自行车有30辆.
鸡兔同笼是中国古代著名趣题之一.大约在1500年前,《孙子算经》中就记载了这个有趣的问题.书中是这样叙述的：“今有雉兔同笼,上有三十五头,下有九十四足,问雉兔各几何?”这四句话的意思是：有若干只鸡兔同在一个笼子里,从上面数,有35个头；从下面数,有94只脚.问笼中各有几只鸡和兔?
这道题无非是把“鸡兔”改为“自行车和三轮车”而已.
最后说明：
我特别把用算术解和用方程解分开,这是因为算术中是不允许有未知数（字母）的,它需要有更高的技巧,方程就是含有未知数（字母）的等式,它属于代数的范畴,相对要容易一些.
希望能够帮到你!
分析：每辆自行车有2个轮子,每辆三轮车有3个轮子.
一、用算术
先确定有多少辆车因为不管自行车还是三轮车每辆车的踏板都是2个,所以三轮车和自行车一共有：
144÷2=72(辆)
假设法：
假设全是自行车那么轮子数：2×72＝144(只) 比总的轮子数少：186－144＝42(只)
三轮车：42÷（3-2）＝42(辆)
自行车：72－42＝30(辆)
二、用方程
设三轮车有x辆,则自行车有72-x辆.
3x+2(72-x)=186
x=186-144 =42（辆）
自行车：
72-42=30（辆）
答：三轮车有42只,自行车有30辆.
鸡兔同笼是中国古代著名趣题之一.大约在1500年前,《孙子算经》中就记载了这个有趣的问题.书中是这样叙述的：“今有雉兔同笼,上有三十五头,下有九十四足,问雉兔各几何?”这四句话的意思是：有若干只鸡兔同在一个笼子里,从上面数,有35个头；从下面数,有94只脚.问笼中各有几只鸡和兔?
这道题无非是把“鸡兔”改为“自行车和三轮车”而已.
最后说明：
我特别把用算术解和用方程解分开,这是因为算术中是不允许有未知数（字母）的,它需要有更高的技巧,方程就是含有未知数（字母）的等式,它属于代数的范畴,相对要容易一些.
希望能够帮到你!
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