How many pounds of potting soil, which costs $0.04 per pound, should be mixed with 20 pounds of nutrient-rich soil, priced at $0.10 per pound, to make a mixture that can be sold for $0.06 per pound?
Thanks in advance!
(p * .04) + (20 * .10) = (20 + p) * .06
To solve this problem, we need to find the amount of potting soil needed to achieve the desired price per pound for the mixture.
Let's say the amount of potting soil needed is x pounds.
The cost of the potting soil is $0.04 per pound, so the cost of x pounds of potting soil is 0.04x dollars.
The cost of the nutrient-rich soil is $0.10 per pound, and there are 20 pounds of it. So the cost of the 20 pounds of nutrient-rich soil is 0.10 * 20 = $2.00.
The total cost of the mixture is the sum of the cost of the potting soil and the cost of the nutrient-rich soil. This total cost should also equal the cost per pound of the mixture multiplied by the total weight of the mixture.
Therefore, we have the equation:
0.04x + 2.00 = 0.06 * (x + 20)
Solving this equation will give us the value of x, which is the amount of potting soil needed.
0.04x + 2.00 = 0.06x + 1.20 (distributing 0.06 to the terms in the parentheses)
2.00 - 1.20 = 0.06x - 0.04x (combining like terms)
0.80 = 0.02x (simplifying)
x = 0.80 / 0.02
x = 40
So, you would need 40 pounds of potting soil to mix with the 20 pounds of nutrient-rich soil.