What is the smallest possible amount of money ?
A grocer in a small business had managed to put aside (apart from his legitimate profits) little sum in dollar bills, half dollars, and quarters, which he kept in eight bags, there being the same number of dollar bills and of each kind of coin in every bag. One night he decided to put the money into only seven bags, again with the same number of each kind of currency in every bag. And the following night he further reduced the number of bags to six, again putting the same number of each kind of currency in every bag. The next night the poor demented miser tried to do the same with five bags, but after hours of trial he utterly failed, had a fit, and died, greatly respected by his neighbors. What is the smallest possible amount of money he had put aside?
He must have had 168 each of dollar bills, half dollars, and quarters, making a total of $294.00. In each of the six bags there would be 28 of each
kind; in each of the seven bags 24 of each kind; and in each of the eight bags, 21 of each kind.
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