How many pounds per acre of diammonium phosphate (18-46-0) are needed to achieve a desired P2O5 application rate of 40 pounds per acre?

To determine how many pounds per acre of diammonium phosphate (18-46-0) are needed to achieve a desired P2O5 application rate of 40 pounds per acre, we need to first understand the composition of diammonium phosphate. The numbers 18-46-0 indicate that the fertilizer contains 18% nitrogen (N), 46% phosphorus (P2O5), and 0% potassium (K2O) by weight.

Since we are focusing on the phosphorus content, we know that 46% of the weight of diammonium phosphate is P2O5. To figure out how much total diammonium phosphate is required to provide 40 pounds of P2O5, you can set up the following calculation:

1. Let ( X ) be the amount of diammonium phosphate needed (in pounds per acre).

2. The phosphorus contribution from diammonium phosphate can be calculated by multiplying the total weight of diammonium phosphate by its P2O5 percentage:

[

0.46 \times X = 40 \text{ pounds of P2O5}

]

3. To solve for ( X ), rearrange the equation:

[

X = \frac