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Difficulty: MediumPercentage Calculations

Complete the statements below with the correct numerical values.

Answer:An upgraded water purification system at a naval facility processes 5,2005,200 gallons of water per hour. This new processing rate represents a 30%30\% increase over the system's previous capacity.

The previous capacity of the system was 【4000】 gallons per hour. The upgrade increased the processing capacity by 【1200】 gallons per hour.

Answer

The previous capacity was 4,000 gallons per hour, and the upgrade increased the capacity by 1,200 gallons per hour.
A 30% increase means the new capacity is 130% of the original capacity. Dividing the new capacity (5,200) by 1.30 gives the original capacity of 4,000 gallons per hour. The numerical increase is the difference between the new and old capacities: 5,200 - 4,000 = 1,200 gallons per hour.

Step-by-Step Solution

1
Set up an equation representing the percentage increase.
Let x be the previous capacity. Since there is a 30% increase, the new capacity is 100% + 30% = 130% of the previous capacity. Therefore, 1.3x = 5200.
To find the original base amount before a percentage increase, we must express the final amount as a percentage of the original.
2
Solve the equation for the previous capacity (x).
x = 5200 / 1.3 = 4000. This is the previous capacity.
Dividing the final amount by the percentage multiplier isolates the original base.
3
Calculate the amount of the capacity increase.
5200 - 4000 = 1200. This is the amount of the increase.
Subtracting the original capacity from the final capacity yields the exact volume added by the upgrade.

Key Concept

Reverse Percentage and Percentage Increase
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Topics

Percentage Calculations

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