A coffee manufacture wants a new blend of coffee that sell for $3.90 per pound by mixing two coffees that sell for $2.75 and #5.oo per pound respectively. What amount of each coffee should be blended to obtain the desired mixture? Assume that the total weight of the desired blend is 100 pounds
amount of $2.75 coffe --- x
amount of $5.00 coffee --- 100-x
solve for x ......
2.75x + 5(100-x) = 3.9(100)
If a pound of coffee costs $12, how many ounces can be bought for $3.90?
To find the amount of each coffee that should be blended to obtain the desired mixture, we can set up a system of equations based on the given information.
Let's assume:
- x pounds of coffee that sells for $2.75 per pound will be used.
- y pounds of coffee that sells for $5.00 per pound will be used.
We can now set up two equations based on the cost and weight of the desired blend:
1. Cost equation: 2.75x + 5.00y = 3.90(100)
This equation represents the cost of the blend, which should be equal to the desired selling price per pound multiplied by the total weight of the desired blend.
2. Weight equation: x + y = 100
This equation represents the total weight of the desired blend, which should be equal to 100 pounds.
Now, we can solve this system of equations to find the values of x and y.
Using the weight equation, we can express x in terms of y:
x = 100 - y
Substituting this expression for x in the cost equation:
2.75(100 - y) + 5.00y = 3.90(100)
275 - 2.75y + 5.00y = 390
2.25y = 115
y = 115 / 2.25
y ≈ 51.11
Now, substitute the value of y back into the weight equation to find x:
x + y = 100
x + 51.11 = 100
x ≈ 48.89
Therefore, the coffee manufacturer should blend approximately 48.89 pounds of coffee that sells for $2.75 per pound and approximately 51.11 pounds of coffee that sells for $5.00 per pound to obtain the desired mixture.