Maria's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Maria $\$ 5.95$ per pound, and type B coffee costs $\$ 4.40$ per pound. This month's blend used three times as many pounds of type B coffee as type $A$, for a total cost of $\$ 689.40$. How many pounds of type $A$ coffee were used?
Number of pounds of type A coffee:

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 \(\boxed{36}\)