To start, denote x as the number of lbs utilized per each coffee type (type A and type B). Further, let ax be the quantity of lbs for type A coffee and bx be the quantity of lbs for type B coffee. So, ax and bx are in units of quantity*lbs.
The cost of type A and type B coffee can be equated as follows:
Cost (A) = 5.95/lb and Cost (B) = 4.65/lb
The key information given ("This month's blend used three times as many pounds of type B coffee as type A, for a total cost of $796.00") can be represented algebraically as follows:
Cost (Blend) = Cost(A)*ax + Cost(B)*bx = $796.00. Since the quantity of type B coffee is 3 times the quantity of type A coffee, it follows that a = 1 and b = 3.
Therefore, 5.95/lb*(x) + 4.65/lb*(3x) = 796--> 5.95/lb*(x) + 13.95/lb*(x) = 796 or (5.95+13.95)(x) = 796.
Therefore, quantity (lbs) = 796/(13.95+5.95) = 796/(19.9) = 40.
Using the previous relation, we know that 3x + x = 40 or 4x = 40. So, the number of lbs for type A coffee utilized in the blend equates to the following:
x = 10 lbs.