For a fixed amount of gas, the following statements may be combined:
The pressure is inversely proportional to the volume
The volume and pressure are directly proportional to the temperature
To give the mathematical expression:
PV/T = constant, where T is the absolute temperature
Substituting the values from the initial and final conditions:
(700 * 500) / (273) = (350 * 220) / T
T = 60.06 K
The temperature change was of -212.94 °C