the manager of a starbucks store plans to mix A grade coffee that cost 9.50 per pound with grade B coffee that cost 7.00 per pound to create a 20 pound blend that will sell for 8.50 a pound. how many pounds of each grade coffee are required?
12 pounds of A grade coffee and 8 pounds of B grade coffee.
amount of A coffee ---- x pounds
amount of B coffee ---- 20-x
9.5x + 7(20-x) = 8.5(20)
9.5x + 140 - 7x = 170
2.5x = 30
x = 12
So 12 pounds of grade A and 8 pounds of grade B
To find out how many pounds of each grade of coffee are required, let's use a system of equations.
Let's assume x pounds of grade A coffee are needed, and y pounds of grade B coffee are needed.
From the given information, we can set up the following equations:
Equation 1: x + y = 20 (since the total blend is 20 pounds)
Equation 2: (9.50 * x) + (7.00 * y) = 8.50 * 20 (since the total cost of the blend should equal the selling price per pound multiplied by the total blend weight)
Let's solve this system of equations:
From Equation 1, we can solve for x: x = 20 - y
Substituting that value of x into Equation 2, we get:
(9.50 * (20 - y)) + (7.00 * y) = 8.50 * 20
Now we can solve for y:
190 - 9.50y + 7y = 170
-2.50y = -20
y = (-20) / (-2.50)
y = 8
Now we can substitute the value of y (8) back into Equation 1 to solve for x:
x + 8 = 20
x = 20 - 8
x = 12
Therefore, the manager needs 12 pounds of grade A coffee and 8 pounds of grade B coffee to make a 20-pound blend.