Question 141010
First, let's compose a combined fraction of the three given, so that we know what fraction of her waking time we have to work with with the other two figures:

{{{w=(1/3)x+(1/5)x+(1/10)x=(19/30)x}}}

That is to say, 19/30 of her time is spent between class, eating, and working out. This leaves 11/30 of her time between studying and doing  other things.
So, let's compose an equality that says the remaining time must equal the remaining fraction of her waking time:
{{{(11/30)x=5.5}}}
{{{x=15}}}. 
This means that she is awake 15 out of every 24 hours. Thus, she sleeps for {{{24-15=9}}} hours per 24 hours.


Check:

class: 5
eating: 3
working out: 1.5
studying: 3
other: 2.5
--------
waking total:15

+sleep:9

waking+sleep total:24.

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