One Tenth

An empty bottle weighs one tenth of its filled weight. If the bottle is partially filled so that it weighs one?

An empty bottle weighs one tenth of its filled weight. If the bottle is partially filled so that it weighs one half of its filled weight, what fraction of the bottle is filled?

Let the weight of the bottle be w.
If it is full, the contents will have a weight of 9w.
Which we derive as follows:
w = 1/10 (w + contents)
10 w = w + contents
9w = contents

We are given: bottle + partial contents = 5w
(5w = 1/2 of 10 w = weight of a full bottle)
So the partial contents = 4w and it is 4/9 full.

(We might interpret the problem to mean that the
partially filled bottle’s weight is half of the total weight
of the partially filled bottle.

In that case,
bottle + partial contents = 2w,
and partial contents = w, and it would be 1/9 full.)

Imagining the Tenth Dimension part 1 of 2

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