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Question
68 boxes of a certain commodity require a shelf-length of 13.6 m. How many boxes of the same commodity would occupy a shelf length of 20.4 m?
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Solution
| Number of Boxes | 68 | x |
| Shelf-length (in m) | 13.6 | 20.4 |
Let x be the number of boxes that occupy a shelf-length of 20.4 m.
\[\text{ If the length of the shelf increases, the number of boxes will also increase .} \]
\[\text{ Therefore, it is a case of direct variation } . \]
\[\frac{68}{x} = \frac{13 . 6}{20 . 4}\]
\[ \Rightarrow 68 \times 20 . 4 = x \times 13 . 6\]
\[ \Rightarrow x = \frac{68 \times 20 . 4}{13 . 6}\]
\[ = \frac{1387 . 2}{13 . 6}\]
\[ = 102\]
\[\text{ Thus, 102 boxes will occupy a shelf - length of } 20 . 4 m .\]
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