Answer :
Sure! Let's determine the most economical fertilizer for your farm by comparing the cost per kilogram for each type of fertilizer. Here are the fertilizers and their prices:
1. Ammonium nitrate ([tex]$NH_4NO_3$[/tex]): [tex]$625 for 25 kg
2. Diammonium hydrogen phosphate ($[/tex]\left(NH_4\right)_2HPO_4[tex]$): $[/tex]55 for 1 kg
3. Ammonia ([tex]$NH_3$[/tex]): [tex]$128 for 50 kg
4. Urea ($[/tex]CO\left(NH_2\right)_2[tex]$): $[/tex]60 for 5 kg
We'll calculate the cost per kilogram for each fertilizer to find out which one is the cheapest. Here are the calculations:
1. Ammonium nitrate ([tex]$NH_4NO_3$[/tex]):
- Total cost: [tex]$625
- Total weight: 25 kg
- Cost per kilogram: $[/tex]625 / 25 kg = [tex]$25.0 per kg
2. Diammonium hydrogen phosphate ($[/tex]\left(NH_4\right)_2HPO_4[tex]$):
- Total cost: $[/tex]55
- Total weight: 1 kg
- Cost per kilogram: [tex]$55 / 1 kg = $[/tex]55.0 per kg
3. Ammonia ([tex]$NH_3$[/tex]):
- Total cost: [tex]$128
- Total weight: 50 kg
- Cost per kilogram: $[/tex]128 / 50 kg = [tex]$2.56 per kg
4. Urea ($[/tex]CO\left(NH_2\right)_2[tex]$):
- Total cost: $[/tex]60
- Total weight: 5 kg
- Cost per kilogram: [tex]$60 / 5 kg = $[/tex]12.0 per kg
Comparing the costs per kilogram for these fertilizers:
- Ammonium nitrate ([tex]$NH_4NO_3$[/tex]): [tex]$25.0 per kg
- Diammonium hydrogen phosphate ($[/tex]\left(NH_4\right)_2HPO_4[tex]$): $[/tex]55.0 per kg
- Ammonia ([tex]$NH_3$[/tex]): [tex]$2.56 per kg
- Urea ($[/tex]CO\left(NH_2\right)_2[tex]$): $[/tex]12.0 per kg
The most economical fertilizer for your farm is Ammonia ([tex]$NH_3$[/tex]) at a cost of $2.56 per kg. This makes it the best choice in terms of cost-efficiency compared to the other options.
1. Ammonium nitrate ([tex]$NH_4NO_3$[/tex]): [tex]$625 for 25 kg
2. Diammonium hydrogen phosphate ($[/tex]\left(NH_4\right)_2HPO_4[tex]$): $[/tex]55 for 1 kg
3. Ammonia ([tex]$NH_3$[/tex]): [tex]$128 for 50 kg
4. Urea ($[/tex]CO\left(NH_2\right)_2[tex]$): $[/tex]60 for 5 kg
We'll calculate the cost per kilogram for each fertilizer to find out which one is the cheapest. Here are the calculations:
1. Ammonium nitrate ([tex]$NH_4NO_3$[/tex]):
- Total cost: [tex]$625
- Total weight: 25 kg
- Cost per kilogram: $[/tex]625 / 25 kg = [tex]$25.0 per kg
2. Diammonium hydrogen phosphate ($[/tex]\left(NH_4\right)_2HPO_4[tex]$):
- Total cost: $[/tex]55
- Total weight: 1 kg
- Cost per kilogram: [tex]$55 / 1 kg = $[/tex]55.0 per kg
3. Ammonia ([tex]$NH_3$[/tex]):
- Total cost: [tex]$128
- Total weight: 50 kg
- Cost per kilogram: $[/tex]128 / 50 kg = [tex]$2.56 per kg
4. Urea ($[/tex]CO\left(NH_2\right)_2[tex]$):
- Total cost: $[/tex]60
- Total weight: 5 kg
- Cost per kilogram: [tex]$60 / 5 kg = $[/tex]12.0 per kg
Comparing the costs per kilogram for these fertilizers:
- Ammonium nitrate ([tex]$NH_4NO_3$[/tex]): [tex]$25.0 per kg
- Diammonium hydrogen phosphate ($[/tex]\left(NH_4\right)_2HPO_4[tex]$): $[/tex]55.0 per kg
- Ammonia ([tex]$NH_3$[/tex]): [tex]$2.56 per kg
- Urea ($[/tex]CO\left(NH_2\right)_2[tex]$): $[/tex]12.0 per kg
The most economical fertilizer for your farm is Ammonia ([tex]$NH_3$[/tex]) at a cost of $2.56 per kg. This makes it the best choice in terms of cost-efficiency compared to the other options.
