You need to find out what the DPI of your existing picture that you want to use is. If it is less than 300, the results are not going to be good. 150 DPI may be passable, but 72 DPI would look awful.
Even by creating a border around it, if the picture is 72 DPI, it is going to look bad when printed out.
But in any event, just multiply by the DPI to get your resolution. For 300 DPI, 35" * 300 = 10,500. 15" * 300 = 4,500. So 10,500 x 4,500 would be the resolution of 300 DPI artwork that would print out to a size of 35" x 15".