a) Since 10.00 g of iodine reacted and produced a compound containing iodine and fluorine with a mass of 144.9g, the difference between these two numbers must represent the mass of fluorine that reacted with the 10.00 g of iodine. 144.9 g - 10.00 g = 134.9 g fluorine.
b) The mass ratio of iodine TO fluorine is 10.00 g iodine/134.9 g fluorine = 0.07413. The mass ratio of fluorine to iodine is 134.9 g/10.00 g = 13.49
c) You can use a proportion here. (10.00 g iodine/144.9 g compound) = (85.2 g iodine/x g compound). Solving for x by cross multiplying gives a mass of compound equal to 1235 g compound or 1230 g with 3 significant figures. This number should be 8.52 times larger than 144.9 since 85.2 g/10.00g = 8.52. It is!
You can also use the mass ratio here. There is 13.49 times as much fluorine as iodine. Multiply the mass of iodine (85.2 g) by 13.49 to get the mass of fluorine and then add this to the mass of iodine (85.2 g). You get the same result.
I hope this helps! :)