A coffee merchant combines coffee that costs $5 per pound with coffee that costs $4.20 per pound. How many pounds of each should be used to make 26 lb of a blend costing $4.80 per pound?

5x + 4.20(26-x) = 4.80*26

To solve this problem, we can use a method called "mixture" or "alligation" to find the ratio of the two coffee types in the blend.

1. Let's assume that x pounds of coffee costing $5 per pound is used.
2. Since the total weight of the blend is 26 pounds, the remaining weight of the blend (26 - x) will consist of coffee costing $4.20 per pound.

Now we can set up an equation based on the cost per pound to determine the ratio:

($5/pound * x pounds) + ($4.20/pound * (26 - x) pounds) = $4.80/pound * 26 pounds

We can now solve this equation algebraically:

5x + 4.20(26 - x) = 4.80 * 26
5x + 109.2 - 4.20x = 124.8
0.8x = 124.8 - 109.2
0.8x = 15.6
x = 15.6 / 0.8
x = 19.5

So, 19.5 pounds of coffee costing $5 per pound should be used.

To find the amount of coffee costing $4.20 per pound, we subtract this value from the total weight of the blend:
26 - 19.5 = 6.5

Therefore, 6.5 pounds of coffee costing $4.20 per pound should be used.