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31 Jul 2025, 10:59
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A specialty fertilizer blend contains 40 percent nitrogen and 60 percent potassium by weight. A different blend contains 20 percent nitrogen and 80 percent phosphorus. When these two blends are combined to create a final mixture, the result contains 35 percent nitrogen. If the final mixture weighs 24 kilograms, how many kilograms of phosphorus does it contain?
A. 3.2
B. 3.6
C. 4
D. 4.8
E. 10.8
A. 3.2
B. 3.6
C. 4
D. 4.8
E. 10.8
31 Jul 2025, 10:59
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Official Solution:
A specialty fertilizer blend contains 40 percent nitrogen and 60 percent potassium by weight. A different blend contains 20 percent nitrogen and 80 percent phosphorus. When these two blends are combined to create a final mixture, the result contains 35 percent nitrogen. If the final mixture weighs 24 kilograms, how many kilograms of phosphorus does it contain?
A. 3.2
B. 3.6
C. 4
D. 4.8
E. 10.8
Let the amount of the first blend be \(x\) kg, so the second blend is \(24 - x\) kg.
The first blend is 40% nitrogen, so it contributes \(0.4x\) kg of nitrogen.
The second blend is 20% nitrogen, so it contributes \(0.2(24 - x)\) kg of nitrogen.
The total nitrogen in the final mixture is 35% of 24, which is 8.4 kg.
Set up the equation:
\(0.4x + 0.2(24 - x) = 8.4\)
\(x = 18\)
That means 18 kg of the first blend and 6 kg of the second. Only the second blend has phosphorus, and it's 80% of that 6 kg. So, phosphorus \(= 0.8 * 6 = 4.8\) kg
Answer: D
A specialty fertilizer blend contains 40 percent nitrogen and 60 percent potassium by weight. A different blend contains 20 percent nitrogen and 80 percent phosphorus. When these two blends are combined to create a final mixture, the result contains 35 percent nitrogen. If the final mixture weighs 24 kilograms, how many kilograms of phosphorus does it contain?
A. 3.2
B. 3.6
C. 4
D. 4.8
E. 10.8
Let the amount of the first blend be \(x\) kg, so the second blend is \(24 - x\) kg.
The first blend is 40% nitrogen, so it contributes \(0.4x\) kg of nitrogen.
The second blend is 20% nitrogen, so it contributes \(0.2(24 - x)\) kg of nitrogen.
The total nitrogen in the final mixture is 35% of 24, which is 8.4 kg.
Set up the equation:
\(0.4x + 0.2(24 - x) = 8.4\)
\(x = 18\)
That means 18 kg of the first blend and 6 kg of the second. Only the second blend has phosphorus, and it's 80% of that 6 kg. So, phosphorus \(= 0.8 * 6 = 4.8\) kg
Answer: D
02 Oct 2025, 04:56
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I don’t quite agree with the solution. "If the final mixture weighs 24 kilograms, how many kilograms of phosphorus does it contain?"- as per my understanding the question is asking for weight of phosphorous in the mixture instead of second blend. It is not clearly mentioned in the question is my understanding.
