Unlocking the Power of Coffee Blending: A Mathematical Journey
How can a coffee distributor create the perfect blend?
What is the ideal combination of Arabian Mocha and Guatemalan Antigua coffee blends needed to create a new blend that sells for $13.61 per pound?
a. 25 pounds of Arabian Mocha and 25 pounds of Guatemalan Antigua
b. 30 pounds of Arabian Mocha and 20 pounds of Guatemalan Antigua
c. 40 pounds of Arabian Mocha and 10 pounds of Guatemalan Antigua
d. 20 pounds of Arabian Mocha and 30 pounds of Guatemalan Antigua
Answer:
To create a mixed blend that sells for $13.61 per pound, the coffee distributor should mix approximately 26 pounds of Arabian Mocha coffee blend and 24 pounds of Guatemalan Antigua coffee blend.
Explanation: In order to achieve the desired selling price of $13.61 per pound for the new coffee blend, the distributor needs to strike a balance between the costs and quantities of the two coffee blends. By setting up and solving a system of equations, we can determine the optimal ratio for the blend.
Let's denote the quantities of Arabian Mocha and Guatemalan Antigua coffee blends as 'a' and 'g' respectively. We know that a + g = 50 (total pounds of coffee) and $12.60*a + $14.70*g = $13.61*50 (total cost of the blend).
Using the elimination method, we can calculate that approximately 26 pounds of Arabian Mocha and 24 pounds of Guatemalan Antigua are needed to achieve the desired selling price.
By understanding the principles of mathematics and applying them to real-world scenarios like coffee blending, we can unlock the power of numbers to optimize our outcomes. Embrace the beauty of problem-solving and elevate your blending skills to new heights!