Of course! To solve this problem, we can use a system of linear equations. I'll guide you step-by-step.
Let's denote the amount of Kenyan French Roast coffee used in the blend by the variable K (in pounds), and the amount of Sumatran coffee by the variable S (also in pounds).
We know that the total weight of the blend is 14 pounds. This information gives us our first equation:
K + S = 14 [Equation 1] (This equation tells us that the sum of the amounts of Kenyan and Sumatran coffee must equal 14 pounds.)
Next, let's think about the cost. We're told that Kenyan French Roast coffee costs $0.700 per pound and Sumatran coffee costs $9.00 per pound. We also know that the blend sells for $8.00 per pound. We can use this information to write another equation based on the total cost of the coffee in the blend:
0.700K + 9.00S = 8.00(14) [Equation 2] (This equation represents the total cost of the coffee in the blend.)
Now, we can solve this system of linear equations. Let's manipulate Equation 1 to solve for one of the variables, say K. From Equation 1, we can write:
K = 14 - S [Equation 3] (We simply subtracted S from both sides of Equation 1.)
Now, let's substitute this expression for K into Equation 2:
0.700(14 - S) + 9.00S = 8.00(14) (We replaced K with 14 - S in Equation 2.)
Now, distribute:
9.8 - 0.700S + 9.00S = 112 (Multiply 0.700 through the parentheses.)
Combine like terms:
9.8 + 8.30S = 112 (Combine the S terms.)
Subtract 9.8 from both sides:
8.30S = 102.2
Now, divide by 8.30 to solve for S:
S ≈ 12.31
Now that we have the approximate value of S, let's plug this back into Equation 3 to find K:
K = 14 - 12.31
K ≈ 1.69
Therefore, to make a 14-pound blend that sells for $8.00 per pound, you should use approximately 1.69 pounds of Kenyan French Roast coffee and approximately 12.31 pounds of Sumatran coffee.