High School

We appreciate your visit to English System vs Metric System tex begin tabular c c c c hline multicolumn 2 r English System multicolumn 2 r Metric System hline Problem. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

**English System vs. Metric System**

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

Answer :

Let's solve the problem step by step for both the English System and the Metric System.

### English System

#### Problem:
How many bricks measuring 3.75 inches wide by 8 inches long are needed to cover a patio measuring 13 feet 6 inches wide by 18 feet 9 inches long?

#### Step 1: Convert dimensions to inches
1. Convert 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]

2. Add the extra inches:
- 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]

#### Step 2: Calculate the area of the patio in square inches
- Area = [tex]\( 162 \, \text{in} \times 225 \, \text{in} = 36,450 \, \text{square inches} \)[/tex]

#### Step 3: Calculate the area covered by one brick in square inches
- Area of one brick = [tex]\( 3.75 \, \text{in} \times 8 \, \text{in} = 30 \, \text{square inches} \)[/tex]

#### Step 4: Calculate the number of bricks needed
- Number of bricks = [tex]\( \frac{36,450 \, \text{square inches}}{30 \, \text{square inches per brick}} \approx 1,215 \)[/tex] bricks

### Metric System

#### Problem:
How many bricks measuring 9.5 cm wide by 20 cm long are needed to cover a patio measuring 4 meters wide by 5 meters long?

#### Step 1: Convert dimensions to centimeters
1. Convert meters to centimeters:
- Width: [tex]\( 4 \, m = 4 \times 100 = 400 \, cm \)[/tex]
- Length: [tex]\( 5 \, m = 5 \times 100 = 500 \, cm \)[/tex]

#### Step 2: Calculate the area of the patio in square centimeters
- Area = [tex]\( 400 \, cm \times 500 \, cm = 200,000 \, \text{square centimeters} \)[/tex]

#### Step 3: Calculate the area covered by one brick in square centimeters
- Area of one brick = [tex]\( 9.5 \, cm \times 20 \, cm = 190 \, \text{square centimeters} \)[/tex]

#### Step 4: Calculate the number of bricks needed
- Number of bricks = [tex]\( \frac{200,000 \, \text{square centimeters}}{190 \, \text{square centimeters per brick}} \approx 1,052.63 \)[/tex]

So, for the English System, you need approximately 1,215 bricks, and for the Metric System, you need about 1,053 bricks (if you round up as you can't have a fraction of a brick in practice, you would need 1,053 bricks).

Thanks for taking the time to read English System vs Metric System tex begin tabular c c c c hline multicolumn 2 r English System multicolumn 2 r Metric System hline Problem. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada

To solve the problem of determining how many bricks are required to cover the patios in both the English and Metric systems, we need to follow these steps:

English System

  1. Convert Measurements to Inches:

    • The patio’s width is given as 13 feet 6 inches. Convert 13 feet to inches:
      [tex]13 \text{ ft} \times 12 \text{ in/ft} = 156 \text{ in}[/tex]
    • Total width in inches:
      [tex]156 \text{ in} + 6 \text{ in} = 162 \text{ in}[/tex]
    • The patio’s length is 18 feet 9 inches. Convert 18 feet to inches:
      [tex]18 \text{ ft} \times 12 \text{ in/ft} = 216 \text{ in}[/tex]
    • Total length in inches:
      [tex]216 \text{ in} + 9 \text{ in} = 225 \text{ in}[/tex]

  2. Calculate the Patio Area in Square Inches:

    • Area = Width [tex]\times[/tex] Length:
      [tex]162 \text{ in} \times 225 \text{ in} = 36450 \text{ in}^2[/tex]

  3. Calculate the Area of a Brick in Square Inches:

    • Brick dimensions are 3.75 inches wide and 8 inches long. Area of a brick:
      [tex]3.75 \text{ in} \times 8 \text{ in} = 30 \text{ in}^2[/tex]

  4. Determine Number of Bricks:

    • Total number of bricks needed:
      [tex]\frac{36450 \text{ in}^2}{30 \text{ in}^2} = 1215 \text{ bricks}[/tex]

Metric System

  1. Convert Measurements to Centimeters:

    • Convert 4 meters to centimeters:
      [tex]4 \text{ m} \times 100 \text{ cm/m} = 400 \text{ cm}[/tex]
    • Convert 5 meters to centimeters:
      [tex]5 \text{ m} \times 100 \text{ cm/m} = 500 \text{ cm}[/tex]

  2. Calculate the Patio Area in Square Centimeters:

    • Area = Width [tex]\times[/tex] Length:
      [tex]400 \text{ cm} \times 500 \text{ cm} = 200000 \text{ cm}^2[/tex]

  3. Calculate the Area of a Brick in Square Centimeters:

    • Brick dimensions are 9.5 cm wide and 20 cm long. Area of a brick:
      [tex]9.5 \text{ cm} \times 20 \text{ cm} = 190 \text{ cm}^2[/tex]

  4. Determine Number of Bricks:

    • Total number of bricks needed:
      [tex]\frac{200000 \text{ cm}^2}{190 \text{ cm}^2} = 1052.63[/tex]
    • Since partial bricks aren’t practical, you would need 1053 bricks.

By completing these steps, we find the number of bricks needed for each system and ensure that all necessary conversions and calculations are accurately performed.

To solve this problem, we need to determine how many bricks are required to cover a given patio area in both the English and Metric systems. Let's break it down step-by-step for each system.

English System

  1. Convert Measurements:
    First, we need to convert the dimensions of the patio from feet to inches, because the brick dimensions are given in 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]

  2. Calculate Total Dimensions in Inches:
    We now add the portion of the measurements expressed in inches:

    • 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]

  3. Calculate the Total Patio Area:
    The area in square inches:
    [tex]\text{Area} = 162 \text{ in.} \times 225 \text{ in.} = 36,450 \text{ square inches.}[/tex]

  4. Calculate the Area of One Brick:
    The area of one brick is:
    [tex]\text{Area of one brick} = 3.75 \text{ in.} \times 8 \text{ in.} = 30 \text{ square inches.}[/tex]

  5. Determine the Number of Bricks Needed:
    Divide the total patio area by the area of one brick to get the number of bricks:
    [tex]\frac{36,450 \text{ square inches}}{30 \text{ square inches}} \approx 1,215 \text{ bricks.}[/tex]

Metric System

  1. Convert Measurements to Centimeters:
    Convert the patio dimensions from meters to centimeters:

    • Width:
      [tex]4 \text{ m} = 4 \times 100 = 400 \text{ cm}[/tex]
    • Length:
      [tex]5 \text{ m} = 5 \times 100 = 500 \text{ cm}[/tex]

  2. Calculate the Total Patio Area in Square Centimeters:
    The area is:
    [tex]\text{Area} = 400 \text{ cm} \times 500 \text{ cm} = 200,000 \text{ square centimeters.}[/tex]

  3. Calculate the Area of One Brick:
    The area of one brick is:
    [tex]\text{Area of one brick} = 9.5 \text{ cm} \times 20 \text{ cm} = 190 \text{ square centimeters.}[/tex]

  4. Determine the Number of Bricks Needed:
    Divide the total patio area by the area of one brick to find the number of bricks:
    [tex]\frac{200,000 \text{ square centimeters}}{190 \text{ square centimeters}} \approx 1,053 \text{ bricks.}[/tex]

Using these steps, we can accurately determine the number of bricks required to cover the patio in both the English and Metric systems.

Other Questions