Step 1 :Let's denote the weight of type A coffee as \(x\) and the weight of type B coffee as \(y\).
Step 2 :We know that the total weight of the coffee blend is 117 pounds, so we can write the equation: \(x + y = 117\).
Step 3 :We also know that the total cost of the blend is $589.85, and the cost per pound of each type of coffee. This gives us the equation: \(4.55x + 5.70y = 589.85\).
Step 4 :We can solve these two equations to find the values of \(x\) and \(y\).
Step 5 :The solution to the equations is \(x = 67\) and \(y = 50\).
Step 6 :So, the number of pounds of type B coffee Deshaun used is \(\boxed{50}\).