A Carpenter several boards of equaling he could 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 four of the original boards how many boards did the Carpenter start with
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.
To determine the number of boards the Carpenter started with, let's break down the information given in the question step by step.
1. The Carpenter could cut each board into 3/5 of its original length.
2. After cutting, the Carpenter had enough pieces left over to make up the same length as four of the original boards.
Let's assume the length of each original board is "L" (a unit of length).
1. The Carpenter cut each board into 3/5 of its length, which means each piece obtained after cutting has a length of (3/5)*L.
2. The number of pieces obtained from each board is the original length divided by the length of each piece, which is (L)/((3/5)*L).
Simplifying this, we get: (L)/(3/5) = (5L)/(3) = (5/3)L.
Therefore, each board can be cut into (5/3) pieces.
Now, the Carpenter has enough leftover pieces to make up the same length as four of the original boards.
Let's represent the number of original boards as "x" (unknown).
The total length of the leftover pieces can be calculated by multiplying the number of leftover pieces by their length.
The length of each leftover piece is (3/5)*L, and the number of leftover pieces can be represented by 4x (since they make up the same length as four original boards).
So, the total length of the leftover pieces is (4x) * ((3/5)*L) = (12/5)xL.
Now, we can set up an equation to solve for the number of original boards:
(12/5)xL = xL
Canceling out the common "L" factor on both sides of the equation, we get:
12/5 = 1
Since this equation is not true, it means our assumption for the number of original boards, "x," is incorrect.
Therefore, based on the given information, it is not possible to determine the exact number of boards the Carpenter started with.