CAPTAIN KIDD AND
THE GOLD COINS
Captain Kidd decided to reward three officers and seven ordinary pirates for outstanding cutthroatedness. He produced a sack containing 140 gold coins and divided them into two unequal piles, giving the larger one to the mates and the smaller to the officers. The officers counted theirs and found that it contained 2 coins more than could be divided equally among themselves. When the mates tried to divide their pile into seven equal shares they were left with a single coin and soon began to squabble over it. They argued so violently that Kidd himself had to step in and command that the remaining coin be given to the officers. Now, if each officer received more booty than each mate, how many coins were in each pile?