The coffee counter charges $9.00 per pound for Kenyan French Roast coffee and $8.00 per pound for Sumatran coffee. How much of each type should be used to make a 20-lb blend that sells for $8.40 per pound?
Answer: Kenyan-8 lb; Sumatran-12 lb.
Can someone help me with how they arrived at this answer? Thank you
To solve this problem, we can set up a system of equations based on the given information.
Let's assume x represents the pounds of Kenyan French Roast coffee used to make the blend, and y represents the pounds of Sumatran coffee used.
From the information provided, we can create the following equations:
1) The total weight of the blend is 20 pounds:
x + y = 20
2) The cost of the blend is $8.40 per pound:
(9x + 8y) / 20 = 8.40
To begin solving this system of equations, we can start by solving the first equation for x:
x = 20 - y
Substitute this value of x into the second equation:
(9(20 - y) + 8y) / 20 = 8.40
Simplify the equation:
(180 - 9y + 8y) / 20 = 8.40
(180 - y) / 20 = 8.40
Multiply both sides of the equation by 20 to get rid of the fraction:
180 - y = 168
Solve for y:
y = 180 - 168
y = 12
Now substitute the value of y back into the first equation to find x:
x = 20 - 12
x = 8
Therefore, the mixture should include 8 pounds of Kenyan French Roast coffee and 12 pounds of Sumatran coffee.
To determine how much of each type of coffee should be used to make the blend, we can set up a system of equations:
Let's represent the amount of Kenyan French Roast coffee used by K, and the amount of Sumatran coffee used by S.
We know that the total weight of the blend is 20 pounds, so we have the equation:
K + S = 20 ---(1)
We also know that the blend sells for $8.40 per pound, so the total value of the blend is $8.40 multiplied by 20 pounds:
8.40 * 20 = 168
The value of the Kenyan French Roast coffee used in the blend is the weight of Kenyan coffee (K) multiplied by the price per pound ($9.00):
9K
The value of the Sumatran coffee used in the blend is the weight of Sumatran coffee (S) multiplied by the price per pound ($8.00):
8S
The equation for the total value of the blend is:
9K + 8S = 168 ---(2)
Now we have a system of equations:
K + S = 20 ---(1)
9K + 8S = 168 ---(2)
To solve this system, we can use the method of substitution or elimination.
Let's use the substitution method and solve equation (1) for K:
K = 20 - S
Now we substitute this value of K into equation (2):
9(20 - S) + 8S = 168
Distribute the 9:
180 - 9S + 8S = 168
Combine like terms:
180 - S = 168
Isolate S by subtracting 180 from both sides:
-S = -12
Multiply by -1 to get S:
S = 12
Now, substitute the value of S back into equation (1) to find K:
K + 12 = 20
K = 20 - 12
K = 8
Therefore, the solution is K = 8 and S = 12.
So, to make a 20-pound blend that sells for $8.40 per pound, you should use 8 pounds of Kenyan French Roast coffee and 12 pounds of Sumatran coffee.
9x + 8(20-x) = 8.4(20)
9x + 160 - 8x = 168
x = 8
20-x = 20-8 = 12