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?

If we let the length of a whole board be 1, then for n boards, we have

2/5 n = 4
n = 10

To solve this problem, let's break it down step by step.

Step 1: Let's assume the length of each original board is 'L' (since it is not mentioned in the question).

Step 2: The carpenter cuts 3/5 of each board, which means he is left with (1 - 3/5) = 2/5 of each board.

Step 3: The length of the leftover pieces is equal to the length of 4 original boards, which means it is equal to 4 * L.

Step 4: Since the carpenter cuts 3/5 of each board and is left with 2/5, the length of the leftover pieces is equal to (2/5) * L.

Step 5: Now we can set up an equation to solve for the number of boards. We can equate the length of the leftover pieces to the length of 4 original boards:

(2/5) * L = 4 * L

Step 6: Simplifying the equation, we can cancel out the 'L' from both sides:

2/5 = 4

This equation is not possible since it is not true. Therefore, there is no valid solution to this problem.