For this question, you should recognize that it is dealing with an ideal gas under changing conditions. The ideal gas law is PV = nRT (equation 1). This can be rearranged to be R = (PV)/(nT) (equation 2). Since R is a constant (the ideal gas constant), you can set two different sets of conditions equal to each other to get (P1V1)/(n1T1) = (P2V2)/(n2T2) (equation 3). This relationship will hold true for all ideal gas scenarios. Sometimes, you may have some conditions which are constant. In that case, you simply eliminate them from the equation. For example, in your question, the number of moles of gas (n) does not change once the balloon is filled. Thus, n1 = n2, so you can eliminate those terms from the equation.
Now that we have it set up, we can see that we have an initial pressure, temperature, and volume; we also have a final temperature and pressure. So, we are solving for the final volume. Note that for gases, your temperature must ALWAYS be in units of Kelvin. To convert from Celsius to Kelvin, you take the temperature in Celsius and add 273.15 to it.
After you make that conversion, you should verify that all units for the pressure and volume are proper (meaning, they are the same in both initial and final conditions) so they will cancel. If they are not proper, you will need to use conversion factors to get the same unit. Once all units are proper, you simply insert the values (with their units) into equation 3 from above, and solve. Make sure your units cancel properly.
