You have seven bags of gold coins. Each bag has the same number of gold coins. One day, you find a bag of 53 coins. You decide to redistribute the number of coins you have so that all eight bags you hold have the same number of coins. You successfully manage to redistribute all the coins, and you also note that you have more than 500 coins. What is the smallest number of coins you could have had before finding the bag of 53 coins?
If you had 8 equal bags with exactly 500 coins, then each bag would have 62.5 coins.
But you can't have half a coin, so you're going to have to have 63 coins in each bag.
63 coins/bag times 8 bags is 504 coins. Subtract the 53 coins you discovered, and
you would have had 451 coins before your lucky discovery.