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Question
In a library 136 copies of a certain book require a shelf-length of 3.4 metre. How many copies of the same book would occupy a shelf-length of 5.1 metres?
Solution
| Number of copies | 136 | x |
| Length the shelf (in m) | 3.4 | 5.1 |
Let x be the number of copies that would occupy a shelf-length of 5.1 m.
\[\text{ Since the number of copies and the length of the shelf are in direct variation, we have: } \]
\[\frac{136}{x} = \frac{3 . 4}{5 . 1}\]
\[ \Rightarrow 136 \times 5 . 1 = x \times 3 . 4\]
\[ \Rightarrow x = \frac{136 \times 5 . 1}{3 . 4}\]
\[ = 204\]
\[\text{ Thus, 204 copies will occupy a shelf of length 5 . 1 m } .\]
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