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# Accounting Riddle

## Accounting Riddle

(OP)
Back in the late 80's, I was given this riddle by an engineer/manager (to test my analytical skills ?), solved it, and have share with many engineers and accountants. No accountant that i gave this riddle to has solved it, but the engineers solved it.

An individual takes a check to the bank to cash. Unbeknownst to the individual, the teller inadvertently exchanges the dollars for cents and the cents for dollars and gives the money to the individual. For example, a $59.35 check is cashed for$35.59.
The individual does not observe/correct the mistake and spends $24.11 in a nearby store. The remaining amount from the cashed check, less$24.11, is twice the original amount of the check.

What is the original check amount/value?

### RE: Accounting Riddle

Do you really mean "The remaining amount from the cashed check, less $24.11, is twice the original amount of the check"? So$24.11 is subtracted twice from the amount of cash the teller gave out at the bank?

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The Help for this program was created in Windows Help format, which depends on a feature that isn't included in this version of Windows.

### RE: Accounting Riddle

I believe the key is setting up the relationship like this:

X = dollar amount of original check.
Y = cents amount of original check.

value of original check = X + Y/100
value that was cashed = Y + X/100

Though I need to know the answer to dgallup's question to take it any further.

### RE: Accounting Riddle

#### Quote (JoshPlum)

I believe the key is setting up the relationship like

It's part of the solution. With these two variable and a single equation you get infinite solution.

The second criteria is that Cent and Dolar value need to be integer; that 0<cent<99 and dollar>0

For that, you need to use trial and error (Excel) to find both values

### RE: Accounting Riddle

I was wondering about that part. I knew I would end up with a nice relationship between the two numbers. But, then thought I'd just try a couple of numbers to see if they worked.

### RE: Accounting Riddle

(OP)
Responding to dgallup . . .

cashed check amount - 24.11 = 2 x original check amount.

JoshPlum is headed in correct direction.

PicoStruc response is correct.

Of all the engineers i gave this riddle to, the quickest response was about 20-minutes by a young engineer working for Bentley Nevada in Minden, NV. i used excel to solve in same time frame.

### RE: Accounting Riddle

"The remaining amount from the cashed check, less $24.11..." This wording implied subtracting the$24.11 twice. Once for the "remaining", and once for the "less".

### RE: Accounting Riddle

The English lesson for this was a LONG time ago and very vague to me, but I think the phrase ", less $24.11," is an appositive for "The remaining amount from the cashed check", and, therefore, the$24.11 is subtracted once.

Good luck,
Latexman

To a ChE, the glass is always full - 1/2 air and 1/2 water.

### RE: Accounting Riddle

Not looking at PicoStruc's post until afterward, I came up with the same result after a few minutes with excel. A table with original dollars in row 1 and original cents in column A. A formula in B2 of =($A2+B$1/100-24.11)/(B$1+$A2/100) then copied to all other cells. Then a bit of conditional formatting to highlight any cell with a value of 2. Only one cell highlighted.

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