A coffee distributor needs to mix a(n) Tanzanian coffee blend that normally sells for $8.40 per pound with a Queen City coffee blend that normally sells for $13.50 per pound to create 80 pounds of a coffee that can sell for $9.93 per pound. How many pounds of each kind of coffee should they mix?
A) Write an equation using the information as it is given above that can be solved to answer the question. Use x as your variable to represent the quantity of Tanzanian coffee blend.
What is the Equation:
B) Answer: They must mix pounds of the Tanzanian Blend pounds of the Queen City Blend. Round your answers to the nearest whole number of pounds.
If there are x lbs of Tanzanian, then the rest (80-x) are Queen.
Now just add up the values of the parts to equal the value of the total.
8.40x + 13.50(80-x) = 9.93*80
A) The equation representing the given information would be:
8.40x + 13.50(80-x) = 9.93(80)
This equation states that the cost of the Tanzanian coffee blend (8.40x) plus the cost of the Queen City coffee blend (13.50(80-x)) should be equal to the cost of the final coffee blend (9.93(80)).
B) To solve the equation:
8.40x + 13.50(80-x) = 9.93(80)
Multiply the values inside the parentheses:
8.40x + 1080 - 13.50x = 794.40
Combine like terms:
-5.10x + 1080 = 794.40
Subtract 1080 from both sides:
-5.10x = -285.60
Divide both sides by -5.10 to solve for x:
x ≈ 56
So, they must mix approximately 56 pounds of the Tanzanian coffee blend and 80 - 56 = 24 pounds of the Queen City coffee blend.
A) To solve this problem, let's first set up an equation using the given information.
Let x represent the quantity of Tanzanian coffee blend to mix. Since they need to create a total of 80 pounds of coffee, the quantity of Queen City coffee blend can be represented as (80 - x).
The cost per pound of Tanzanian coffee blend is $8.40, and the cost per pound of Queen City coffee blend is $13.50. Therefore, the total cost of the Tanzanian coffee blend is (8.4x) and the total cost of the Queen City coffee blend is (13.5 * (80 - x)).
To create a coffee blend that sells for $9.93 per pound, the total cost of the blend should be equal to the total cost per pound multiplied by the total quantity. Therefore, the equation can be written as:
(8.4x) + (13.5 * (80 - x)) = (9.93 * 80)
B) To find the quantities of each blend, we can solve the equation.
Let's simplify the equation:
8.4x + (13.5 * 80) - (13.5x) = 9.93 * 80
8.4x + 1080 - 13.5x = 794.4
Combine like terms:
-5.1x + 1080 = 794.4
Now, let's solve for x:
-5.1x = 794.4 - 1080
-5.1x = -285.6
x = -285.6 / -5.1
x ≈ 56
The quantity of Tanzanian coffee blend should be approximately 56 pounds.
To find the quantity of the Queen City coffee blend, we can substitute the value of x into the original equation:
(80 - x) ≈ 80 - 56
(80 - x) ≈ 24
The quantity of the Queen City coffee blend should be approximately 24 pounds.