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?
To solve this problem, we need to find the number of original boards the carpenter started with. Let's work step by step:
Let's assume the length of each original board is L.
The carpenter cuts 3/5 of each board, which means he cuts 3/5 * L = (3L/5) from each board.
After cutting the boards, the carpenter is left with pieces that make up the same length as 4 of the original boards.
If 4 original boards have a combined length of 4L, then the pieces the carpenter is left with should also have a combined length of 4L.
Since the carpenter cuts 3/5 of each board, we can calculate the total length of the leftover pieces as (3L/5) * number of original boards.
Now we can set up an equation to find the number of original boards:
(3L/5) * number of original boards = 4L
To simplify the equation, we can cancel out the L terms:
(3/5) * number of original boards = 4
To isolate the number of original boards, we can multiply both sides of the equation by 5/3:
number of original boards = (4 * 5) / 3
number of original boards = 20/3
Since we cannot have a fraction of a board, we need to round the answer up to the nearest whole number because the carpenter cannot have a fraction of a board.
Therefore, the carpenter started with 7 boards (rounding up from 20/3).
(2/5) x = 4
times 5
2x = 20
x = 10