How many pounds of coffee worth $7.50 per pound must be blended with coffee worth $9.50 per pound to make a mixture of 12 pounds of coffee worth $8.00 per pound?
the value of the coffee in each part must add up to the whole. So,
7.50x + 9.50(12-x) = 8.00(12)
x = 9
so,
9 lbs at $7.50 and
3 lbs at $9.50
To find out how many pounds of coffee worth $7.50 per pound must be blended with coffee worth $9.50 per pound to make a mixture of 12 pounds of coffee worth $8.00 per pound, we can set up an equation.
Let's assume x represents the number of pounds of coffee worth $7.50 per pound.
The total amount of coffee, when blended, is 12 pounds. Therefore, the amount of coffee worth $9.50 per pound is (12 - x) pounds.
Now, let's calculate the total value of the coffee worth $7.50 per pound and $9.50 per pound.
The value of the coffee worth $7.50 per pound is found by multiplying the number of pounds (x) by the price per pound ($7.50), giving us 7.50x dollars.
The value of the coffee worth $9.50 per pound is found by multiplying the number of pounds (12 - x) by the price per pound ($9.50), giving us 9.50(12 - x) dollars.
The total value of the mixture is found by multiplying the total pounds of coffee (12) by the price per pound ($8.00), giving us 8.00 * 12 dollars.
As the total value of the mixture is the sum of the values of the individual coffees, we have the equation:
7.50x + 9.50(12 - x) = 8.00 * 12
Now, we can solve this equation to find the value of x.
7.50x + 9.50(12 - x) = 96
7.50x + 114 - 9.50x = 96
-2x + 114 = 96
-2x = 96 - 114
-2x = -18
To solve for x, divide both sides by -2:
x = -18 / -2
x = 9
Therefore, to make a mixture of 12 pounds of coffee worth $8.00 per pound, you need 9 pounds of coffee worth $7.50 per pound, and (12 - 9) = 3 pounds of coffee worth $9.50 per pound.