A carpenter has several boards of equal length. He cuts 3/5 of each board. After cutting the boards, the carpenter notices 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?
The Correct Answer and Explanation is:
To solve this problem, let’s define the variables and carefully work through the logic:
Let’s Define the Variables:
Let each board have a total length of 1 unit (for simplicity).
The carpenter cuts 3/5 of each board, which means 2/5 of each board remains.
Let x be the number of original boards.
So, the leftover piece from each board is 2/5 units in length.
If the carpenter starts with x boards, then the total leftover length is: x×25x \times \frac{2}{5}
We’re told that this leftover total length is equal to 4 full boards, or simply 4 units in total.
Set up the Equation:
x×25=4x \times \frac{2}{5} = 4
Solve for x:
x=4×52=202=10x = \frac{4 \times 5}{2} = \frac{20}{2} = 10
✅ Correct Answer: 10 boards
300-Word Explanation:
To find out how many boards the carpenter started with, we begin by interpreting the key information. Each board is cut so that 3/5 is removed and 2/5 is left. The crucial piece of information is that the total leftover wood—which consists of the 2/5 segments from each board—adds up to the equivalent of 4 full boards.
For ease of calculation, we assume each board is 1 unit long. This makes it simple to calculate fractions of the board. If each board is 1 unit, then cutting off 3/5 leaves 2/5 of a unit per board. So, every time the carpenter cuts a board, he has 2/5 of a board left.
Let x represent the number of boards the carpenter starts with. From each of the x boards, there remains 2/5 of a board. Therefore, the total leftover length is x × 2/5.
We are told that all the leftover pieces combined are equal in length to 4 full boards (i.e., 4 units). So we can write the equation: x×25=4x \times \frac{2}{5} = 4
Multiplying both sides by 5 to eliminate the denominator: 2x=202x = 20
Dividing both sides by 2: x=10x = 10
So, the carpenter originally had 10 boards. This problem is a classic example of how fractions and simple algebra can be applied to real-life situations to determine totals when parts are removed or left behind.