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?
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To solve this problem, we can set up an equation based on the information given.
Let's assume the original length of each board is 'L'.
The carpenter cuts 3/5 of each board, which leaves 2/5 of each board unused. So, the total length of the unused pieces is (2/5) * L for each board.
The carpenter then notices that he has enough unused pieces to make up the same length as 4 of the original boards. This means the total length of the unused pieces is equal to 4L.
We can set up the equation as follows:
(2/5) * L * x = 4L
Where 'x' represents the number of original boards the carpenter started with.
Now, let's solve the equation to find the value of 'x':
(2/5) * L * x = 4L
Multiplying both sides by 5/2 to eliminate the fraction:
x = (4L * 5) / (2L)
x = 20L / 2L
x = 10
Therefore, the carpenter started with 10 boards.