Aballoon, whose volume at 23°c is 535 ml, is heated to 46°c. assuming the pressure and amount of gas remain constant, what is the volume of the balloon at 46°c?

This problem requires a certain equation.  That equation is V1/T1=V2/T2, where V1 is your initial volume (535 mL in this case), T1 is your initial temperature in Kelvin(23 degrees C = 296 K), V2 is your final volume (unknown), and T2 is your final temperature (46 degrees C = 319 K). By plugging in these values, the equation looks like this: 535/296=V2/319.  Now multiply both sides of the equation by 319, and your final answer is V2= 576.6 mL

Yes you are correct use the scientific method