Math CentralQuandaries & Queries


Question from Yanly, a teacher:

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?

Hi Yanly,

Suppose that there are $n$ boards, each of length $l$ units. The carpenter cuts off 3/5 of each board so he is left with $\frac25 \times l \times n$ units of length. This is the same length as $4 \times l$ units.

Solve for $n.$


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