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Zorluk: OrtaPercents and Percent Change

An environmental study monitored the water volume of two reservoirs, Reservoir A and Reservoir B. In June, the water volume of Reservoir A was 20%20\% greater than the water volume of Reservoir B. By August, the water volume of Reservoir A had decreased by 15%15\%, while the water volume of Reservoir B had increased by 10%10\%. If the water volume of Reservoir A in August was 10.210.2 million gallons, what was the water volume of Reservoir B in June, in millions of gallons?

  1. A
    8.5
  2. B
    9.6
  3. 10.0Cevap
  4. D
    14.4

Cevap

The water volume of Reservoir B in June was 10.0 million gallons.
The correct answer is the value that represents Reservoir B's volume in June. Let BB represent Reservoir B's water volume in June. Since Reservoir A's June volume was 20%20\% greater than Reservoir B's, it is represented as 1.20B1.20B. Between June and August, Reservoir A's volume decreased by 15%15\%, so its August volume is 85%85\% of its June volume, which is 0.85×1.20B=1.02B0.85 \times 1.20B = 1.02B. Setting this equal to the given August volume of 10.210.2 million gallons yields 1.02B=10.21.02B = 10.2. Solving for BB gives B=10.0B = 10.0 million gallons.

Adım Adım Çözüm

1
Define a variable for the unknown quantity and express Reservoir A's volume in June.
Let BB represent the water volume of Reservoir B in June. Since Reservoir A's June volume was 20%20\% greater than Reservoir B's, the volume of Reservoir A in June is 1.20B1.20B.
This establishes the relationship between the initial volumes of the two reservoirs.
2
Determine Reservoir A's volume in August in terms of the variable BB.
Since Reservoir A's volume decreased by 15%15\% by August, its new volume is 85%85\% of its June volume. Thus, the volume in August is 0.85×1.20B=1.02B0.85 \times 1.20B = 1.02B.
This represents the two-stage percentage change for Reservoir A.
3
Solve for the variable BB using the given August volume.
Set the expression for Reservoir A's August volume equal to 10.210.2 million gallons: 1.02B=10.21.02B = 10.2. Dividing both sides by 1.021.02 gives B=10.0B = 10.0 million gallons.
This finds the initial volume of Reservoir B.

Anahtar Kavram

Multi-step percentage change and setting up equations to solve for initial values.
Tahmini Süre:1m 30s
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Konular

Percents and Percent Change

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