SOLUTION: The volume of a quantity of an ideal gas was held constant. The inital pressure and temperature were 400 torr and 80 K. What would be the final temperature if the final pressure wa

The volume of a quantity of an ideal gas was 
held constant. The inital pressure and 
temperature were 400 torr and 80°K. What
would be the final temperature if the final 
pressure was 300 torr?

The combined gas law is the best one to learn 
instead of separate Charles' and Boyles' laws.
It is

  pv       PV
------ = ------
   t        T

where the little letters are the measures 
of pressure p, volume v, and temperature 
t, at one time, and the big letters on the 
right P, V, and T are those measurements
at another time. 

Since the volume of the quantity was held 
constant, v = V, and we can just divide both 
sides by both sides by v = V and get

 p     P
--- = ---
 t     T

which just eliminates the quantity held
constant, namely the Volume from the
combined gas law above.

>>...The inital pressure and temperature
were 400 torr and 80 K...<<

So plug in little p = 400 and little t = 80

 400     P
----- = ---
  80     T


>>...the final pressure was 300 torr...<<

So plug in 300 for big P:

 400     300
----- = -----
  80      T

Solve for big T:

Since it's in the form "fraction = fraction",
you can cross-multiply:

(Upper left)(lower right) = (Upper right)(lower left)

                     400T = (300)(80)
                     400T = 24000
                        T = 24000/400
                        T = 60°K

Edwin