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?

Question

Mathematics

Darby

19 January, 12:15

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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Answers (1)

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Steven Davies · Answer 1

I'll call the number of original sized boards x.

So the length of all the leftover pieces together would be

(1) x - (3/5) x = (2/5) x

Now, the third sentence is the important part. It says that all the leftover parts add up to 4 board lengths.

(2/5) x = 4

Multiply each side by 5/2 to solve for x.

x = 10

x was the number of original sized boards, so he started with 10 boards.