Question

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?

Answer 1

Upon cutting 3/5 of each board, the carpenter finds that the leftover pieces amount to the length of 4 original boards. Calculating the equation (2/5)x = 4 and solving for x, we find out that the carpenter originally had 10 boards.

Step-by-step explanation:

The question involves determining the original number of boards a carpenter had before cutting them and noticing that the leftover pieces equaled the length of 4 original boards. We know that the carpenter cuts 3/5 of each board, meaning that 2/5 of each board is leftover. If the leftovers equate to 4 whole boards, we can set up an equation to solve for the original number of boards (let's call this number 'x').

Since 2/5 of each board is leftover, and the leftovers make 4 full boards, we can represent this situation with the equation (2/5)x = 4. To solve for 'x', we divide both sides of the equation by 2/5 which is equivalent to multiplying by its reciprocal (5/2), yielding x = 4 × (5/2) = 10. Therefore, the carpenter started with 10 boards.

Answer 2

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.
:D