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Difficulty: MediumPercentage Calculations

Determine the final inventory count and the net percentage change by filling in the blanks.

Answer:A military supply depot initially stored 5,0005,000 tactical vests. During a regional exercise, the inventory was reduced by 30%30\%. Afterward, a new shipment increased the remaining stock by 40%40\%. The depot now holds 【4900】 tactical vests. Compared to the original inventory, this represents a net 【decrease】 of 【2】\%.

Answer

The depot now holds 4,900 vests, representing a net decrease of 2%.
The final inventory is 4,9004,900 vests, which is 100100 vests fewer than the original 5,0005,000. This equates to a net decrease of 2%2\%. In successive percentage problems, it is crucial to recalculate the base amount for each step.

Step-by-Step Solution

1
Calculate the inventory after the initial 30%30\% reduction.
5,000−(0.30×5,000)=5,000−1,500=3,5005,000 - (0.30 \times 5,000) = 5,000 - 1,500 = 3,500 vests.
The first event reduces the starting stock by 30%30\%, establishing a new base amount for the subsequent calculation.
2
Calculate the inventory after the 40%40\% increase.
3,500+(0.40×3,500)=3,500+1,400=4,9003,500 + (0.40 \times 3,500) = 3,500 + 1,400 = 4,900 vests.
The 40%40\% increase applies only to the remaining stock (3,5003,500), not the original 5,0005,000.
3
Determine the net change from the original inventory.
5,000−4,900=1005,000 - 4,900 = 100 vests fewer than the original.
Comparing the final inventory (4,9004,900) to the original inventory (5,0005,000) reveals a net decrease.
4
Calculate the net percentage change.
(1005,000)×100%=0.02×100%=2%(\frac{100}{5,000}) \times 100\% = 0.02 \times 100\% = 2\%.
The percentage change is found by dividing the absolute change by the original base amount, then multiplying by 100%100\%.

Key Concept

Successive Percentages and Changing Base Values
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Topics

Percentage Calculations

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