4. A carpenter has several boards of equal length. He cuts \( \frac{3}{5} \) 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?

Let's denote the length of each board as \( L \) and the number of boards the carpenter starts with as \( n \). After cutting \( \frac{3}{5} \) of each board, the length of the remaining piece of one board is: \[ L - \frac{3}{5}L = \frac{2}{5}L \] The total length of the remaining pieces from all \( n \) boards is: \[ n \times \frac{2}{5}L = \frac{2n}{5}L \] According to the problem, this total length is equal to the length of 4 original boards: \[ \frac{2n}{5}L = 4L \] To solve for \( n \), we can divide both sides by \( L \) (assuming \( L \neq 0 \)): \[ \frac{2n}{5} = 4 \] Next, multiply both sides by \( 5 \) to eliminate the fraction: \[ 2n = 20 \] Now, divide by \( 2 \): \[ n = 10 \] Thus, the carpenter started with **10 boards**.