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The coin bag

The coin bag

A group of friends find a bag with 56 coins. They do not know very well how to distribute them since they cannot do it in equal parts so one of them comes up with a solution:

Each of us will throw a coin in the air, if it goes expensive, it will take 5 coins and if it goes cross, it will take 6 coins.

Once the distribution was over, there was no money left over and we know that among those who received 6 coins there were two brothers.

How many of them received 5 coins and how many of them received 6 coins?

Solution

If we call X to the number of friends who received 5 coins and Y to the number of friends who received 6 coins, we get the following equation: 56 = 5x + 6y

Since we know that X and Y must be integer values, we can try different values ​​of X until we get an integer value of Y considering that as stated in the statement there are at least two people with 6 coins.

So the solution is that 4 friends received 5 coins, and 6 friends received 6 coins.