Questions: You are a contractor installing a brick sidewalk. The brick portion of the sidewalk will occupy an area 100 feet long by 4 feet wide. Each brick will occupy an area 8 inches long by 4 inches wide. What is the minimum number of bricks you will need to build the sidewalk? 150 208 400 816 1,800

You are a contractor installing a brick sidewalk. The brick portion of the sidewalk will occupy an area 100 feet long by 4 feet wide. Each brick will occupy an area 8 inches long by 4 inches wide. What is the minimum number of bricks you will need to build the sidewalk? 150 208 400 816 1,800
Transcript text: You are a contractor installing a brick sidewalk. The brick portion of the sidewalk will occupy an area 100 feet long by 4 feet wide. Each brick will occupy an area 8 inches long by 4 inches wide. What is the minimum number of bricks you will need to build the sidewalk? 150 208 400 816 1,800
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Solution

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Solution Steps

Step 1: Convert the dimensions of the sidewalk and bricks to the same unit
  • The sidewalk is 100 feet long and 4 feet wide. Convert feet to inches:
    • \( 100 \text{ feet} = 100 \times 12 = 1200 \text{ inches} \)
    • \( 4 \text{ feet} = 4 \times 12 = 48 \text{ inches} \)
Step 2: Calculate the area of the sidewalk and the area of one brick
  • Area of the sidewalk:
    • \( 1200 \text{ inches} \times 48 \text{ inches} = 57600 \text{ square inches} \)
  • Area of one brick:
    • \( 8 \text{ inches} \times 4 \text{ inches} = 32 \text{ square inches} \)
Step 3: Determine the minimum number of bricks needed
  • Divide the area of the sidewalk by the area of one brick:
    • \( \frac{57600 \text{ square inches}}{32 \text{ square inches}} = 1800 \text{ bricks} \)

Final Answer

\(\boxed{1800}\)

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