A carpenter has several boards of equal length. He cuts 3/5 of each board. After cutting the boards, the Carpender 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 Carpender start with?
there are b boards
after cutting, there are lengths totalling b * 2/5 left over
so, after cutting 5 boards, he has enough leftovers to make 2 original lengths.
...
To solve this problem, let's use algebra.
Let's say the length of each original board is x.
Since the carpenter cuts 3/5 of each board, the length of each remaining piece is (1 - 3/5) * x, which simplifies to (2/5) * x.
The carpenter notices that he has enough remaining pieces to make up the same length as four of the original boards. So, the combined length of the remaining pieces is equal to 4 times the length of each original board.
Given that, we can write the equation:
(2/5) * x * number of boards = 4 * x
Now, let's solve for the number of boards:
(2/5) * x * number of boards = 4 * x
Dividing both sides of the equation by x:
(2/5) * number of boards = 4
Multiply both sides of the equation by 5/2:
number of boards = (4 * 5) / 2
number of boards = 20 / 2
number of boards = 10
Therefore, the carpenter started with 10 boards.