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 break down the problem step by step: 1. **Initial Setup:** - Let \( L \) be the length of each board. - Suppose the carpenter starts with \( N \) boards. 2. **Cutting the Boards:** - He cuts \( \frac{3}{5} \) of each board, which means he removes a length of \( \frac{3}{5}L \) from each board. - The leftover piece from each board is \( L - \frac{3}{5}L = \frac{2}{5}L \). 3. **Total Leftover Length:** - Since there are \( N \) boards, the total leftover length is \( N \times \frac{2}{5}L \). 4. **Given Condition:** - The total leftover length is equal to the length of 4 original boards, which is \( 4L \). - Therefore, \( N \times \frac{2}{5}L = 4L \). 5. **Solving for \( N \):** \[ N \times \frac{2}{5}L = 4L \\ N \times \frac{2}{5} = 4 \\ N = 4 \times \frac{5}{2} \\ N = 10 \] So, the carpenter started with **10 boards**. **Answer:** 10