The Coffee Counter charges $11.00 per pound for Kenyan French Roast coffee and $15.00 per pound for Sumatran coffee.
How much of each type should be used to make aa 24 pound blend that sells for $13.00 per pound?
12, 12 you’re welcome!!
To solve the problem, let's use a system of equations.
Let x be the pounds of Kenyan French Roast coffee used, and y be the pounds of Sumatran coffee used.
We can set up the following equations:
Equation 1: x + y = 24 (The total weight of the blend is 24 pounds)
Equation 2: 11x + 15y = 13 * 24 (The total cost of the blend is $13 per pound)
To solve the system of equations, we can use the method of substitution.
First, let's solve Equation 1 for x:
x = 24 - y
Substitute this expression for x in Equation 2:
11(24 - y) + 15y = 312
264 - 11y + 15y = 312
4y = 48
y = 12
Now substitute the value of y back into Equation 1 to find x:
x + 12 = 24
x = 12
Therefore, 12 pounds of Kenyan French Roast coffee and 12 pounds of Sumatran coffee should be used to make a 24-pound blend that sells for $13.00 per pound.
To solve this problem, we can use a system of equations. Let's assign variables to the unknown quantities:
Let's say x represents the pounds of Kenyan French Roast coffee.
And y represents the pounds of Sumatran coffee.
We know that the total weight of the blend is 24 pounds, so we can write the equation:
x + y = 24 -- Equation 1
We also know that the cost per pound of the blend is $13.00. This means that the cost of the Kenyan French Roast coffee plus the cost of the Sumatran coffee should equal the cost of the blend. We can write the equation:
11x + 15y = 13(24) -- Equation 2
Now we have a system of equations (Equation 1 and Equation 2) that we can solve simultaneously.
Let's start by solving Equation 1 for one of the variables:
x = 24 - y
Now substitute this expression for x in Equation 2:
11(24 - y) + 15y = 13(24)
Distribute the 11:
264 - 11y + 15y = 312
Combine like terms:
4y = 312 - 264
4y = 48
Divide by 4:
y = 48 / 4
y = 12
Now that we know the value of y is 12, we can substitute it back into Equation 1 to find the value of x:
x + 12 = 24
x = 24 - 12
x = 12
Therefore, you would need 12 pounds of Kenyan French Roast coffee and 12 pounds of Sumatran coffee to make a 24 pound blend that sells for $13.00 per pound.
amount of Kenyan coffee ---- x
amount of Sumatran coffee -- 24-x
11x + 15(24-x) = 13(24)
solve for x