456 000 has been rounded to the nearest thousand.
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Suppose that the height (in centimeters) of a candle is a linear function of
the amount of time (in hours) it has been burning.
Let x be the amount of time in hours
Let y be the heoght of a candle in centimeters
The two points are then as (9,24.5) and (23,17.5).
Now plug in x=21, we get
Thus the height of the candle after 21 hours is 18.5 centimeters.
Example:
This suggests two solutions,
and 
.
However, upon plugging these solutions back into the equation, you get
which checks out, but
does not because
is defined only for 
(assuming you're looking for real solutions only). So, we call an extraneous solution, and the complete solution set (over the real numbers) is .
This suggests two solutions,
However, upon plugging these solutions back into the equation, you get
which checks out, but
does not because
If the letters are considered distinct, then the number of permutations is 
.
If we count either C as the same character, then we would be double-counting - to correct this, we would simply divided by the number of ways we can choose C from the available characters, or
.
If we count either C as the same character, then we would be double-counting - to correct this, we would simply divided by the number of ways we can choose C from the available characters, or