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Difficulty: MediumRectangular Area Applications

A homeowner is applying a protective sealant to a rectangular wooden patio that completely surrounds a rectangular swimming pool. The overall dimensions of the patio and pool together are 40 feet40\text{ feet} long and 30 feet30\text{ feet} wide. The swimming pool inside measures 25 feet25\text{ feet} long and 15 feet15\text{ feet} wide. One gallon of sealant covers exactly 150 square feet150\text{ square feet} of wood and costs $28\$28. If the homeowner must purchase whole gallons of sealant, what is the total cost, in dollars, of the sealant required for the wooden patio?

Answer: 168 $

Answer

The total cost of the sealant is $168.
The net area of the patio is found by subtracting the pool area from the total area (1200−375=825 sq ft1200 - 375 = 825\text{ sq ft}). Dividing this by the coverage rate (825÷150=5.5825 \div 150 = 5.5) shows how many gallons are needed. Since partial gallons are not sold, this rounds up to 6 gallons6\text{ gallons}. At $28\$28 per gallon, the cost is 6×28=$1686 \times 28 = \$168.

Step-by-Step Solution

1
Calculate the total combined area of the patio and the pool.
1200 square feet1200\text{ square feet}
To find the gross area before removing the inner section, multiply the overall length by the width (40×3040 \times 30).
2
Calculate the area of the swimming pool.
375 square feet375\text{ square feet}
To find the area that does not require sealant, multiply the pool's length by its width (25×1525 \times 15).
3
Subtract the pool area from the total area.
825 square feet825\text{ square feet}
To find the net area of the wooden patio that actually needs sealant (1200−3751200 - 375).
4
Divide the net area by the coverage of one gallon of sealant.
5.5 gallons5.5\text{ gallons}
To determine the exact volume of sealant required (825÷150825 \div 150).
5
Round up to the next whole gallon.
6 gallons6\text{ gallons}
Because the homeowner must purchase whole gallons, any fraction requires buying an additional full gallon.
6
Multiply the number of gallons by the cost per gallon.
$168\$168
To calculate the final total cost (6×286 \times 28).

Key Concept

Calculating net rectangular area by subtracting an inner rectangle from an outer boundary, and applying real-world constraints such as rounding up to whole purchasing units.
Estimated Time:1m 30s
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Topics

Rectangular Area Applications

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