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# Can you Find the error?

bukaida
Tom gets \$50 from his father every week for his out of pocket expenses.For this he has to submit an account at the end of every week. But last week he could not reconcile his statement of accounts, The same is as follows:
 Code: Day                          Spent                      Balance                                Monday                         \$ 20                         \$ 30                                Wednesday                    \$ 15                         \$ 15                                Thursday                       \$ 09                         \$ 06                                Saturday                       \$ 06                         \$ 00                                                                ------------                  ----------                                                     TOTAL      \$ 50                         \$ 51                                                                 ------------                 -------------

Help Tom in reconciling the discrepancy.
zacky
By following and looking at the format it looks like Tom spend more than what he gets on the balance. Which I assume since he did not submit he's statement of expenses on accounts, when the next Monday comes, he gets \$50 again which only he can consume is \$49.

Regardless of what break down may come up to, all in all in two weeks he got \$100.

On first week is \$51 which he spend more than what he got while on second week is \$49.
Peterssidan
It took me a while to realize but the Balance column shows how much he has left to spend this week at the end of the day. Calculating the sum of this column doesn't give any useful information. Tom should instead be looking at the \$ 00 at the end of the column which means he didn't use too much or too little.
Bikerman
..is the correct answer. This is a classic case of apples and pears - confusing two different things when measuring and comparing. The problem here is made easier to see by selecting different values for expenditure....So, for example:
Expenditure.........Balance.
12.......................38
12.......................26
12.......................14
12.......................2
2.........................0
Clearly the balance column now sums to way more than 50
spinout
Say you have some cars - and the marking is 100 to 140 on the rooftops.... A common idea for most people is to count 140 - 100 = 40 cars, when it actually is 41 of them. A balance is a balance, but you can add balances. The whole concept of balance accounting is Assets eq capital plus loans. Movements under a period are accounted on other (higher) types of accounts, where the sign is shifted called result accounts. So Asserts are counted as debit (incr) while capital and loans are (incr) credit -> but result accounts like sales vs costs are vice versa. Sales are incr in credit and cost are incr in debit.
This means is you look into a business system and see a result report having the minus sign in the bottom it is showing more credit that debit, and that means a positive result for the period. Basic ekonomic tradition just.
cabenqc
Well, that is a philosophy question.
Not a mathematics question.
We shouldn't try to solve that in a mathematical way.
Peterssidan
 cabenqc wrote: Well, that is a philosophy question. Not a mathematics question. We shouldn't try to solve that in a mathematical way.

It's not a philosophical question. Tom obviously did a mistake.
bukaida
Peterssidan wrote:
 cabenqc wrote: Well, that is a philosophy question. Not a mathematics question. We shouldn't try to solve that in a mathematical way.

It's not a philosophical question. Tom obviously did a mistake.

Right, there is a logical error in analyzing the problem. The error is in mathematical logic not philosophical.
Afaceinthematrix
 spinout wrote: Say you have some cars - and the marking is 100 to 140 on the rooftops.... A common idea for most people is to count 140 - 100 = 40 cars, when it actually is 41 of them. A balance is a balance, but you can add balances. The whole concept of balance accounting is Assets eq capital plus loans. Movements under a period are accounted on other (higher) types of accounts, where the sign is shifted called result accounts. So Asserts are counted as debit (incr) while capital and loans are (incr) credit -> but result accounts like sales vs costs are vice versa. Sales are incr in credit and cost are incr in debit. This means is you look into a business system and see a result report having the minus sign in the bottom it is showing more credit that debit, and that means a positive result for the period. Basic ekonomic tradition just.

 Peterssidan wrote: It took me a while to realize but the Balance column shows how much he has left to spend this week at the end of the day. Calculating the sum of this column doesn't give any useful information. Tom should instead be looking at the \$ 00 at the end of the column which means he didn't use too much or too little.

Neither of those has anything to do with the mistake. The mistake is simple: if you start with 50 dollars and spend 1 dollar a day, then your balance is 49, then 48, then 47 etc. which will add up to 25*49 = 1225 which is certainly not 50. BTW, 25*49 comes from the formula (I will explain this since we don't have Latex) that the sum of the first n numbers is [n(n+1)]/2.

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