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

I'll call the number of original sized boards x.

So the length of all the leftover pieces together would be

(1) x - (3/5) x = (2/5) x

Now, the third sentence is the important part. It says that all the leftover parts add up to 4 board lengths.

(2/5) x = 4

Multiply each side by 5/2 to solve for x.

x = 10

x was the number of original sized boards, so he started with 10 boards.