# Thread: For the Mathmaticians Among Us

1. For the Mathmaticians Among Us
My smart alec grandson hit me with this:

A borrows \$50 each from B and C= \$100
A gives B and D \$1 each, keeps \$1
A owes B and C \$49 each =\$98
\$98 + \$1 = \$99
Where did the other dollar go?

2.
This is an old problem... it hasn't gone anywhere....

A has \$97 in merchandise + \$1 +(\$1 to B + \$1 to C)= \$98 + \$2= \$100

3.
Really more an accounting question than a math question.

I glaze over when the math and physics posters here get into it, but for this trained accountant the debits and credits described above are quite clear.

4.
I know the dollar did not disappear but being neither an accountant, mathematician or physicist, it is over my head.
I hire people to do my taxes.

5.
A has the dollar. If s/he returns the item and gets a full refund of \$97, s/he'll have \$98, which is exactly enough to pay pack B and C.

The mathematical sleight of hand was adding the money owed (\$98) to the money in A's hand (\$1). Those are the wrong things to add up if you're looking at where the money went; instead one should look at who is holding each portion of the money.

At the end of the day B and C only have \$1 each, not \$49 each. A also has \$1, so that's \$3 total between the three of them; the shop where A bought the item has the other \$97.

6.
Originally Posted by lonewolf
My smart alec grandson hit me with this:

A borrows \$50 each from B and C= \$100
A gives B and D \$1 each, keeps \$1
A owes B and C \$49 each =\$98
\$98 + \$1 = \$99
Where did the other dollar go?
A owes B and C \$49 each =\$98 ???

Uh, no....he borrowed \$50 from C and gave nothing back to C.
That's a red herring. What he owes (\$50 + \$49 = \$99) has nothing to do with where the \$3 is, which is in the pockets of A, B, and D. \$97 is spent and 3 are waiting to buy gum.

7.
And as we all know, or as Abbott and Costello taught us, you can get two \$10's for a \$5.

8.
Yeah, I think D owes everyone a buck three fifty.

9.
Originally Posted by trackCanuck
A owes B and C \$49 each =\$98 ???

Uh, no....he borrowed \$50 from C and gave nothing back to C.
That's a red herring. What he owes (\$50 + \$49 = \$99) has nothing to do with where the \$3 is, which is in the pockets of A, B, and D. \$97 is spent and 3 are waiting to buy gum.
Typo...A gives B and C \$1 payment...

10.
Originally Posted by lonewolf
Typo...A gives B and C \$1 payment...
Ok. Looking at the original information again:

A borrows \$50 each from B and C= \$100
A gives B and D \$1 each, keeps \$1
A owes B and C \$49 each =\$98
\$98 + \$1 = \$99
Where did the other dollar go?

\$98 + \$1 = \$99 - What he owes plus his third of the change does not account for all the money, nor should we think it does.

To account for the money, look at what was spent and where the change is now. That's the equation that matter. \$97 plus A's B's and C's shares of the \$3 change = \$100.

Nothing different from what Conor wrote earlier, just noticed.

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