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, 2012

Algebra Difficulty 1.7 Junior Find the answer Canada

A string has been cut into 4 pieces, all of different lengths. The length of each piece is 2 times the length of the next smaller piece. What fraction of the original string is the longest piece?

Pick one

Solution

Let $L$ be the length of the string.

If $x$ is the length of the shortest piece, then since each of the other pieces is twice the length of the next smaller piece, then the lengths of the remaining pieces are $2x$ , $4x$ , and $8x$ .

Since these four pieces make up the full length of the string, then $x+2x+4x+8x=L$ or $15x=L$ and so $x = \frac{1}{15}L$ .

Thus, the longest piece has length $8x = \frac{8}{15}L$ , which is $\frac{8}{15}$ of the length of the string.

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.