A person needs to prepare 130 pounds of
blended coffee beans for $5.27 per pound. He plans to do this by blending
together a high-quality bean costing $6.50 per pound and a cheaper bean at $2.50 per pound. To the nearest pound,
find how much high-quality coffee bean
and how much cheaper coffee bean he should blend.
see related problem links below. Same problms, different numbers.
To find the amount of high-quality coffee beans and cheaper coffee beans that need to be blended, we can set up a system of equations.
Let's say the amount of high-quality beans the person needs to blend is represented by 'x' pounds, and the amount of cheaper beans is represented by 'y' pounds.
From the given information, we can set up the following equations:
Equation 1: x + y = 130 (the total amount of blended coffee beans is 130 pounds)
Equation 2: (6.50 * x) + (2.50 * y) = (5.27 * 130) (the cost of the blended coffee beans is $5.27 per pound)
Now, we can solve the system of equations to find the values of 'x' and 'y'.
First, let's rearrange Equation 1 to solve for 'x':
x = 130 - y
Substitute this value of 'x' in Equation 2:
(6.50 * (130 - y)) + (2.50 * y) = (5.27 * 130)
Now, simplify and solve the equation for 'y':
845 - 6.50y + 2.50y = 685.10
-4y = -159.90
y ≈ 39.98
To the nearest pound, 'y' is approximately 40 pounds.
Now substitute this value of 'y' back into Equation 1 to find 'x':
x + 40 = 130
x = 130 - 40
x = 90
To the nearest pound, 'x' is approximately 90 pounds.
Therefore, the person should blend approximately 90 pounds of high-quality coffee beans and 40 pounds of cheaper coffee beans.