A coffee distributor needs to mix a(n) Organic Free Trade coffee blend that normally sells for $8.30 per pound with a Rift Valley coffee blend that normally sells for $13.90 per pound to create 80 pounds of a coffee that can sell for $10.82 per pound. How many pounds of each kind of coffee should they mix?
Answer: They must mix
______pounds of the Organic Free Trade Blend
______pounds of the Rift Valley Blend.
Round your answers to the nearest whole number of pounds.
Let's assume that the number of pounds of the Organic Free Trade coffee blend is represented by variable A, and the number of pounds of the Rift Valley coffee blend is represented by variable B.
We can set up two equations based on the given information:
Equation 1: A + B = 80 (since the total weight of the coffee blend is 80 pounds)
Equation 2: (8.30A + 13.90B) / 80 = 10.82 (since the average selling price per pound of the mixture is $10.82)
To solve this system of equations, we can rearrange Equation 2 to solve for A:
8.30A + 13.90B = 10.82 * 80
8.30A + 13.90B = 865.60
Now we can express A in terms of B by rearranging Equation 1:
A = 80 - B
Substituting this value of A into Equation 2:
8.30(80 - B) + 13.90B = 865.60
664 - 8.30B + 13.90B = 865.60
5.60B = 201.60
B ≈ 36.00
Rounding to the nearest whole number, B ≈ 36 pounds.
Now we can substitute this value of B back into Equation 1 to find A:
A + 36 = 80
A ≈ 44
Rounding to the nearest whole number, A ≈ 44 pounds.
Therefore, they must mix approximately 44 pounds of the Organic Free Trade Blend and 36 pounds of the Rift Valley Blend.
To solve this problem, we can use a system of linear equations. Let's assign variables to the unknowns:
Let x be the number of pounds of the Organic Free Trade Blend.
Let y be the number of pounds of the Rift Valley Blend.
Now let's set up the equations based on the given information.
Equation 1: The total weight of the coffee blend is 80 pounds.
x + y = 80
Equation 2: The cost of the coffee blend is $10.82 per pound.
(8.30x + 13.90y) / 80 = 10.82
To solve this system of equations, we can use a method called substitution or elimination.
Let's use substitution method to solve this system of equations.
First, solve equation 1 for x:
x = 80 - y
Now substitute the value of x in equation 2:
(8.30(80 - y) + 13.90y) / 80 = 10.82
Simplify the equation by distributing and combining like terms:
664 - 8.30y + 13.90y = 865.60
Combine the y terms:
5.60y = 201.60
Divide both sides by 5.60 to solve for y:
y = 36
Now, substitute the value of y back into equation 1 to solve for x:
x + 36 = 80
x = 80 - 36
x = 44
Therefore, they must mix 44 pounds of the Organic Free Trade Blend and 36 pounds of the Rift Valley Blend.
Very similar to your previous alcohol mixture problem that I did for you.
Follow my procedure and let me know what you get.
hint:
let the amount of $8.30 coffee be x pounds
then the amount of $13.90 coffee be 80-x pounds