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 200 coins. What is the smallest number of coins you could have had before finding the bag of 53 coins?
7 bags each have 29 coins to start .
Let x be the final coin coint in the EIGHT bags 8x > 200 so x >25
Now 53 - x has to be divisible by the remaining 7 bags
trial and error
26 53 - 26 = 27 nope
27 53 - 27 = 26 nope
32 53-32 = 21 Yes ! x = 32 = final count in the 8 bags
(8 * 32 -53 ) / 7 = inital coin count in the 7 bags = 29 coins/bag