Acarpenter has several boards of equal length, he cuts 3/5 of of each board. after cutting the boards the carpenter notices that he has enough left over to make up the same length as 4 of the original boards. how many boards did the carpenter start with?

4 of the original boards have a summed length of 20 units. 5 x 4 = 20.
Since 2/5 is left from each board, you simply add them until the 2's add to 20.So, 2 x 10 = 20. Hence, there are 10 2/5 boards.That's just 4 of the boards that the 2/5 make up, but that should also mean that there are 10 3/5 boards as well.

30/5 + 20/5 = 50/5
Reduction = 10

The carpenter started with 10 5/5 boards.