Question

How many kilograms of soil supplement that costs 7.00 per kilogram must be mixed with 20 kg of aluminum nitrate that costs 3.50 per kilogram to make a fertilizer that costs 4.50 per kilogram?

Answer 1

To determine the amount of soil supplement needed, set up a weighted average equation and solve for x. 8 kilograms of soil supplement must be mixed with 20 kilograms of aluminum nitrate.

Step-by-step explanation:

To determine the amount of soil supplement needed to make a fertilizer that costs 4.50 per kilogram, we can set up a weighted average equation. Let x represent the amount of soil supplement needed in kilograms. The cost of the soil supplement is $7 per kilogram, and the cost of the aluminum nitrate is $3.50 per kilogram. The average cost is $4.50 per kilogram, so we can express the equation as:

7x + 3.50(20) = 4.50(x + 20)

Simplifying the equation:

7x + 70 = 4.50x + 90

2.5x = 20

x = 8

Therefore, 8 kilograms of soil supplement must be mixed with 20 kilograms of aluminum nitrate.