Step 1 :For the first problem, set up the equation: \(x(x - 8) = 240\)
Step 2 :Solve for x: \(x = 20\)
Step 3 :\(\boxed{20}\) ft is the width that will cause the farmer to purchase the land.
Step 4 :For the second problem, set up the equation: \((n - 4)(2n + 5) = 15\)
Step 5 :Solve for n: \(n = 5\)
Step 6 :\(\boxed{5}\) is the number for the second problem.