Author Topic: 美国人真的不会算术  (Read 6237 times)

fzy

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美国人真的不会算术
« on: 二月 12, 2013, 03:18:25 pm »
看到一篇关于要不要取消penny的文章,其中有这样一段:

The United States penny costs 2.4 cents to make. But eliminating it would result in greater use of the five-cent coin, the nickel, which costs 11.2 cents to produce. So the American penny survives, at least for the time being.

其实如果取消penny,二舍三入到5分,nickle的使用也会减少的。

万精油

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Re: 美国人真的不会算术
« Reply #1 on: 二月 13, 2013, 02:30:59 pm »
假设Mod10以后,1分到9分的出现率相同,那么有Penny与
没有Penny(二舍三入到5分),Nickle 的使用率应该是一样
的。只不过原来是5,6,7,8,9都需要Nickle,现在是3,
4,5,6,7需要Nickle. 但是,取消Penny后,所有的Penny
开销没有了,所以还是取消划算。

具体的算一下,A=2.4 (Penny的造价),B=11.2(Nickle的造价)
有Penny的情况是(从1到9)
A+2*A+3*A+4*A+B+B+A+B+2*A+B+3*A+B+4*A = 104
没有Penny的情况是(从1到9)
0+0+B+B+B+B+B+0+0=56


fzy

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Re: 美国人真的不会算术
« Reply #2 on: 二月 14, 2013, 09:30:51 am »
You are right. Usage of all other coins remain the same. I thought we could save some coins since 98, 99 cents round to dollar, but no.

万精油

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Re: 美国人真的不会算术
« Reply #3 on: 二月 14, 2013, 10:43:58 am »
Quote
I thought we could save some coins since 98, 99 cents round to dollar, but no.

This is very tricky. On the surface, looks like we can save some quarters when rounding up 98 and 99 cents. However, we need to add an extra quarter at 23,24, 48,49, 73,74 cents (which were not needed before rounding). This cancel out the six quarters we saved from rounding up 98 and 99.

This problem is getting more and more interesting.

packman

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Re: 美国人真的不会算术
« Reply #4 on: 二月 14, 2013, 06:34:56 pm »
This is not difficult. Just use an Excel spreadsheet. Assume equal distribution from $0.01 to $1.00, you can list the coins need to represent that with or without penny (round to nearest 5), by using the smallest amount of coins. By plug in the unit cost of each coin, you can calculate how much saving (or waste) by eliminating penny. Below is the example. Sorry about the  bad formatting.

   with penny            without penny      
Cents   1   5   10   25   5   10   25
1   1                  
2   2                  
3   3            1      
4   4            1      
5      1         1      
6   1   1         1      
7   2   1         1      
8   3   1            1   
9   4   1            1   
10         1         1   
11   1      1         1   
12   2      1         1   
13   3      1      1   1   
14   4      1      1   1   
15      1   1      1   1   
16   1   1   1      1   1   
17   2   1   1      1   1   
18   3   1   1         2   
19   4   1   1         2   
20         2         2   
.........................................................                     
90      1   1   3   1   1   3
91   1   1   1   3   1   1   3
92   2   1   1   3   1   1   3
93   3   1   1   3       2   3
94   4   1   1   3      2   3
95         2   3      2   3
96   1      2   3      2   3
97   2      2   3      2   3
98   3      2   3   0   0   0
99   4      2   3   0   0   0
100   0   0   0   0   0   0   0
简单==完美

packman

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Re: 美国人真的不会算术
« Reply #5 on: 二月 14, 2013, 06:42:43 pm »
It will be tricky if you consider "change". For example, 0.23 can be represented as 2 dime + 3 penny, or 1 quarter less 2 penny.

But the above excel approach can still be used.
简单==完美

packman

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Re: 美国人真的不会算术
« Reply #6 on: 二月 15, 2013, 11:13:28 am »
The attached worksheet (in pdf format, forum does not allow excel upload) illustrates the potential savings by eliminating penny.
Notes are written at the top of the sheet.

assuming the cost of making a coin is:
penny -- $0.024  (given in previous posts)
nickel -- $0.012 (given in previous posts)
dime -- $0.10 (assuming face value, could be wrong)
quarter -- $0.25 (assuming face value, could be wrong)

I can update the worksheet if anyone know the exact cost of making each coin.

Overall, about 4.4% saving can be achieved.
简单==完美