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\begin{tabular}{|c|c|c|c|}
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\multicolumn{2}{|r|}{English System} & \multicolumn{2}{|r|}{Metric System} \\
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Problem: & How many bricks 3.75 in. wide [tex]$\times$[/tex] 8 in. long are required to cover a patio 13 ft 6 in. wide by 18 ft 9 in. long? & Problem: & How many bricks 9.5 cm wide [tex]$\times$[/tex] 20 cm long are required to cover a patio 4 meters wide by 5 meters long? \\
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Step 1. & First, find the total width and length of the patio in inches. & Step 1. & First, find the area of the patio in square cm. \\
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Step 1a. & \begin{tabular}{l}
Convert the portion of width and length that is expressed in feet to inches: \\
width: [tex]$13 \text{ ft} = 13 \times 12 = 156 \text{ in.}$[/tex] \\
length: [tex]$18 \text{ ft} = 18 \times 12 = 216 \text{ in.}$[/tex]
\end{tabular} & Step 1a. & \begin{tabular}{l}
Convert the width and length in meters to cm: \\
width: [tex]$4 \text{ m} = 4 \times 100 = 400 \text{ cm}$[/tex] \\
length: [tex]$5 \text{ m} = 5 \times 100 = 500 \text{ cm}$[/tex]
\end{tabular} \\
\hline
Step 1b. & \begin{tabular}{l}
Add these values to the portion of the width and length of the patio expressed in inches to find totals: \\
total width: [tex]$156 \text{ in.} + 6 \text{ in.} = 162 \text{ in.}$[/tex] \\
total length: [tex]$216 \text{ in.} + 9 \text{ in.} = 225 \text{ in.}$[/tex]
\end{tabular} & Step 2. & \begin{tabular}{l}
Find the area of the patio in square cm by multiplying its width by its length: \\
[tex]$400 \text{ cm} \times 500 \text{ cm} = 200,000 \text{ cm}^2$[/tex]
\end{tabular} \\
\hline
\end{tabular}

Answer :

Sure, let's go through the process step-by-step!

### English System

1. Convert dimensions from feet and inches to total inches:
- Width: The patio is 13 feet 6 inches wide.
- First, convert the feet into inches: [tex]\(13 \times 12 = 156\)[/tex] inches.
- Add the remaining 6 inches: [tex]\(156 + 6 = 162\)[/tex] inches for the total width.
- Length: The patio is 18 feet 9 inches long.
- First, convert the feet into inches: [tex]\(18 \times 12 = 216\)[/tex] inches.
- Add the remaining 9 inches: [tex]\(216 + 9 = 225\)[/tex] inches for the total length.

2. Calculate the area of the patio in square inches:
- Multiply the total width by the total length: [tex]\(162 \times 225 = 36,450\)[/tex] square inches for the total area of the patio.

3. Determine the dimensions of one brick:
- A brick is 3.75 inches wide and 8 inches long.

4. Calculate the area of one brick in square inches:
- Multiply the brick’s width and length: [tex]\(3.75 \times 8 = 30\)[/tex] square inches for each brick.

5. Determine the number of bricks required:
- Divide the total patio area by the area of one brick: [tex]\(\text{Number of bricks} = \lceil \frac{36,450}{30} \rceil = 1,215\)[/tex].
- You would need 1,215 bricks to cover the patio.

### Metric System

1. Convert dimensions from meters to centimeters:
- Width: The patio is 4 meters wide.
- Convert meters to centimeters: [tex]\(4 \times 100 = 400\)[/tex] cm.
- Length: The patio is 5 meters long.
- Convert meters to centimeters: [tex]\(5 \times 100 = 500\)[/tex] cm.

2. Calculate the area of the patio in square centimeters:
- Multiply the total width by the total length: [tex]\(400 \times 500 = 200,000\)[/tex] square cm for the patio area.

3. Determine the dimensions of one brick:
- A brick is 9.5 cm wide and 20 cm long.

4. Calculate the area of one brick in square centimeters:
- Multiply the brick’s width by its length: [tex]\(9.5 \times 20 = 190\)[/tex] square cm for each brick.

5. Calculate the number of bricks required:
- Divide the total patio area by the area of one brick: [tex]\(\text{Number of bricks} = \lceil \frac{200,000}{190} \rceil = 1,053\)[/tex].
- You would need 1,053 bricks to cover the patio.

These calculations show how many bricks you would need for each system to cover the patio completely.

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