The possible width is anything up to 18 ft.
Work Step by Step
If the cheerleaders can use no more than 96 ft of trim around the banner, the perimeter of the banner must be less than or equal to 96 ft. The perimeter is the sum of the lengths plus the widths. Let w be the possible width. $2(30)+2w\leq96\longrightarrow$ multiply $60+2w\leq96\longrightarrow$ subtract 60 from each side $60+2w-60\leq96-60\longrightarrow$ subtract $2w\leq36\longrightarrow$ divide each side by 2 $2w\div2\leq36\div2\longrightarrow$ divide $w\leq18$