HELP heres a math problem ; give me a formula for it please;;; a carpenter has several boards of equal length. he cuts 3/5 of each board.after cutting the boards , he notices that he has enough pieces left over to make up the same length as 4 of the origional boards. how many boards did the carpenter start with?
2/5 n = 4
n = 10
To solve this problem, let's break it down step by step:
Let's say the original length of each board is represented by "x."
According to the problem, the carpenter cuts 3/5 of each board. So, after cutting, each board remaining will be 2/5 of the original length.
Now, the problem states that the length of the pieces left over is equal to the length of 4 original boards. Therefore, the total length of the leftover pieces will be 4 times the original length of each board.
Let's represent the total length of the leftover pieces as "L."
We can set up the equation:
L = 4 * x
Now, let's think about the length of the leftover pieces. Each remaining board is 2/5 of the original length, so the total length of the leftover pieces will be 2/5 of the total length of the boards the carpenter started with.
Since the carpenter started with "n" number of boards, the total length of the leftover pieces can also be represented as:
L = (2/5) * n * x
Now, we can equate the two expressions for L:
4 * x = (2/5) * n * x
We can cancel out the "x" terms on both sides of the equation:
4 = (2/5) * n
To isolate "n," we can multiply both sides of the equation by 5/2:
n = 4 * (5/2)
Simplifying:
n = 10
Hence, the carpenter started with 10 boards.