Answered

A trash compactor can reduce the volume of its contents to 0.350 their original value. neglecting the mass of air expelled, by what factor is the density of the rubbish increased?

Answer :

Let m = the mass of the trash
Let V =  original volume
The original density is m/V

After the volume is compressed, it is 0.35 of the original volume.
The mass remains the same, so the new density is
m/(0.35V) = 2.857V

The increase in original density is 2.857 = 285.7% (approximately 300%)

Answer: The density increases by a factor of 2.85 (or a factor of about 3)

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