Question

Difficulty: MediumCalculating Percentages of Quantities

Read the scenario and calculate the final remaining amount. Enter only the numerical value in the blank.

Answer:A naval shipyard crew is assigned to apply a specialized anti-corrosion coating to 3,2003,200 square feet of a submarine's hull. During the first week of the project, the crew successfully coats 45%45\% of the total area. In the second week, due to bad weather, they only manage to coat 25%25\% of the remaining uncoated area. Based on this progress, exactly 【1320】 square feet of the hull still need to be coated.

Answer

1320
The correct calculation requires adjusting the base for the second percentage. First, find 45%45\% of the original 3,2003,200 square feet, which is 1,4401,440 square feet. This leaves 1,7601,760 square feet uncoated. The second week's progress is 25%25\% of that remaining 1,7601,760 square feet, equaling 440440 square feet. Subtracting this from the 1,7601,760 gives a final uncoated area of 1,3201,320 square feet.

Step-by-Step Solution

1
Calculate the area coated during the first week.
3,200×0.45=1,4403,200 \times 0.45 = 1,440 square feet.
To find the initial amount completed, multiply the total area by the first week's completion percentage.
2
Calculate the remaining uncoated area after the first week.
3,200−1,440=1,7603,200 - 1,440 = 1,760 square feet.
Subtract the coated area from the total area to establish the new base amount for the second week's calculation.
3
Calculate the area coated during the second week.
1,760×0.25=4401,760 \times 0.25 = 440 square feet.
Multiply the remaining uncoated area by the second week's completion percentage.
4
Calculate the final remaining uncoated area.
1,760−440=1,3201,760 - 440 = 1,320 square feet.
Subtract the second week's coated area from the previously remaining area to find the final answer.

Key Concept

Calculating successive percentages by identifying the correct base quantity for each step.
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