Examkin

Question

Difficulty: HardRectangular Area Applications

A city planner is designing a rectangular park that features a central grassy area measuring 150 feet150 \text{ feet} long and 90 feet90 \text{ feet} wide. A uniform concrete walkway that is 6 feet6 \text{ feet} wide will be constructed around the entire outer perimeter of the grassy area. If the concrete paving costs $12.50\$12.50 per square yard, what is the total cost, in dollars, of the paving material required for the walkway?

Answer: 4200 dollars

Answer

4200
The correct cost is found by determining the total area of the walkway by subtracting the inner grass area from the outer total area (16,524−13,500=3,024 sq ft16,524 - 13,500 = 3,024 \text{ sq ft}), converting to square yards by dividing by 9 (336 sq yd336 \text{ sq yd}), and multiplying by the price of $12.50\$12.50 per square yard.

Step-by-Step Solution

1
Determine the outer dimensions of the total area.
Outer length = 162 ft, Outer width = 102 ft.
The walkway is 6 feet wide and borders all sides. Therefore, 6 feet must be added to both ends of the length (150+6+6=162150 + 6 + 6 = 162) and both sides of the width (90+6+6=10290 + 6 + 6 = 102).
2
Calculate the area of the outer rectangle.
16,524 sq ft
Area is length multiplied by width: 162×102=16,524162 \times 102 = 16,524.
3
Calculate the area of the inner grassy rectangle.
13,500 sq ft
Using the given inner dimensions: 150×90=13,500150 \times 90 = 13,500.
4
Find the area of the walkway.
3,024 sq ft
Subtract the inner area from the outer area: 16,524−13,500=3,02416,524 - 13,500 = 3,024.
5
Convert the walkway area from square feet to square yards.
336 sq yd
There are 3×3=93 \times 3 = 9 square feet in one square yard. Divide the area by 9: 3,024÷9=3363,024 \div 9 = 336.
6
Calculate the total cost.
$4,200
Multiply the area in square yards by the cost per square yard: 336×12.50=4,200336 \times 12.50 = 4,200.

Key Concept

Calculating subtractive rectangular area and converting square units for cost analysis.
Rate this question

Topics

Rectangular Area Applications

More questions from this topic