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Zorluk: OrtaPercentages, Percent Change, and Interest

In 2024, a municipal water treatment plant processed water using two filtration systems: System A and System B. System A processed 60%60\% of the plant's total water volume, and System B processed the remaining 40%40\%. In 2025, the volume of water processed by System A increased by 20%20\%, while the volume of water processed by System B decreased by 15%15\%. What was the net percentage change in the total volume of water processed by the plant from 2024 to 2025?

  1. An increase of 6%6\%Cevap
  2. B
    An increase of 5%5\%
  3. C
    A decrease of 1%1\%
  4. D
    An increase of 2.5%2.5\%
  5. E
    An increase of 3.5%3.5\%

Cevap

An increase of 6%6\%
To find the net percentage change, calculate the weighted contribution of each component change relative to the initial total. Assuming a total volume of 100100 units in 2024, System A processed 6060 units and System B processed 4040 units. In 2025, System A processed 60×1.20=7260 \times 1.20 = 72 units, and System B processed 40×0.85=3440 \times 0.85 = 34 units. The new total volume is 72+34=10672 + 34 = 106 units. The net change from 100100 to 106106 represents an increase of 6%6\%.

Adım Adım Çözüm

1
Assume a convenient baseline total volume for 2024.
Let the total volume in 2024 be 100100 units. System A processes 6060 units and System B processes 4040 units.
Choosing 100100 simplifies percentage calculations.
2
Calculate the volume processed by each system in 2025.
System A: 60×(1+0.20)=7260 \times (1 + 0.20) = 72 units.
System B: 40×(1−0.15)=3440 \times (1 - 0.15) = 34 units.
Apply the respective percentage increase and decrease to each system's 2024 volume.
3
Calculate the total volume processed in 2025 and the net percentage change.
Total 2025 volume = 72+34=10672 + 34 = 106 units.
Net change = 106−100=+6106 - 100 = +6 units, which is an increase of 6100×100%=6%\frac{6}{100} \times 100\% = 6\%.
Compare the new total volume to the original baseline total volume.

Anahtar Kavram

Weighted Percent Change
Tahmini Süre:1m 30s
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Konular

Percentages, Percent Change, and Interest

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