the medieval spice merchant wants to blend some garlic powder, which costs 38 cents per pound, with 7 pounds of ground pepper, which costs 44 cents per pound, to create a big batch of medieval smelling salt worth exactly 40 cents per pound. How many pounds of the garlic powder should he use?
Let x be the number of pounds of garlic powder needed.
The total cost of the garlic powder is 0.38x, the total cost of the ground pepper is 0.44 * 7 = 3.08, and the total cost of the blended mixture is 0.40(x + 7).
Since the total cost of the blended mixture must equal the sum of the costs of the garlic powder and the ground pepper, we have the equation:
0.38x + 3.08 = 0.40(x + 7)
0.38x + 3.08 = 0.40x + 2.80
0.28 = 0.02x
x = 14
Therefore, the medieval spice merchant should use 14 pounds of garlic powder.