Step 1 :Let's denote the number of pounds of type A coffee as 'a' and the number of pounds of type B coffee as 'b'.
Step 2 :We know that the cost of type A coffee is $5.95 per pound and the cost of type B coffee is $4.40 per pound. We also know that the total cost of the blend is $689.40. This gives us the first equation: \(5.95a + 4.40b = 689.40\)
Step 3 :We also know that the blend used three times as many pounds of type B coffee as type A. This gives us the second equation: \(b = 3a\)
Step 4 :We can solve this system of equations to find the values of 'a' and 'b'.
Step 5 :The solution to the system of equations is: \(a = 36.0000000000000\), \(b = 108.000000000000\)
Step 6 :Final Answer: The number of pounds of type A coffee used is \(\boxed{36}\)