Let's go through the problem step-by-step: --- ## **Given Data:** - Total length of wall: **80 ft** - Height of each brick: **8 inches** (which is **8/12 = 2/3 ft**) - Height of each row of bricks: **8 inches** (same brick height) - Overhead door width: **12 ft** - Overhead door height: **8 ft** (since it's a door) - Number of rows: **3** - Mortar joints thickness: **.8 inches** (which is **.8/12 = 2/15 ft**) --- ## **Step 1: Determine total number of rows** The wall has **3 rows** of bricks, each **8 inches** high. - Height of the total wall (from the figure): 17'-4" (which is **17 + 4/12 = 17.333 ft**) Check if this matches the sum of the brick rows: - 3 rows × 8 inches = 24 inches = 2 ft Since the total height is 17'-4" (~17.33 ft), the remaining height could be mortar joints and other structural elements. But for calculating the bricks, focus on the height of the rows. --- ## **Step 2: Calculate the length of the wall excluding the door** - Total length: 80 ft - Width of door: 12 ft Remaining length of wall: \[ 80\, ft - 12\, ft = 68\, ft \] --- ## **Step 3: Determine the number of bricks per row** ### 3.1: Brick length with mortar joints - Brick length: Unknown, but we can find the number of bricks by dividing the total length (excluding door) by the length of one brick plus mortar. ### 3.2: Brick and mortar dimensions - Brick length: \( L_b \) (unknown) - Mortar joint between bricks: .8 in = .8/12 ≈ .067 ft ### 3.3: Number of bricks in a row (excluding the door) Total length of wall without door: 68 ft Number of bricks in a row: \[ N_b = \frac{\text{Total length of wall without door}}{\text{Brick length} + \text{Mortar joint}} \] But since the problem gives the total number of bricks required for the entire wall, and the illustration shows the pattern, we can estimate the number of bricks per row. --- ## **Step 4: Find the total number of bricks needed** From the figure, the pattern shows: - 3 brick courses - The wall has bricks arranged in patterns, but for simplicity, assume uniform brick size and pattern. Assuming: - Each brick is approximately 8 inches long (standard size), with mortar joints of .8 inches between bricks. Number of bricks per foot: \[ \frac{12\, in}{8\, in + .8\, in} \approx \frac{12}{8.8} \approx 1.36 \] Total bricks in one row (excluding door): \[ \text{Bricks per row} = 68\, ft \times 1.36 \approx 92.48 \approx 92 \text{ bricks} \] Total bricks for 3 rows: \[ 92 \times 3 = 276 \] --- ## **Step 5: Calculate total mortar joints** - Each row has approximately 92 bricks, so: Number of mortar joints per row: \[ 92 - 1 = 91 \] Total mortar joints across all rows: \[ 91 \times 3 = 273 \] --- ## **Step 6: Total mortar joint length** - Total mortar length in joints: \[ 273 \times .8\, in = 218.4\, in \] Convert to feet: \[ \frac{218.4}{12} \approx 18.2\, ft \] --- ## **Step 7: Final calculation** ### **Total length of bricks:** - Total length of bricks: \[ \text{Number of bricks} \times \text{brick length} \] Assuming each brick is 8 inches (standard): \[ 276 \times 8\, in = 2208\, in \] Convert to feet: \[ \frac{2208}{12} = 184\, ft \] ### **Total length of mortar:** \[ 18.2\, ft \] ### **Total length of bricks + mortar:** \[ 184\, ft + 18.2\, ft \approx 202.2\, ft \] --- ## **Final Answer:** The total length of bricks required is approximately **184 ft**. --- **Note:** The calculation is based on typical brick sizes and pattern assumptions. Actual values may vary depending on specific brick sizes and pattern details in the figure.

Let's re-evaluate the problem and provide a clear, step-by-step solution based on the information given. ## **Problem Overview** We need to calculate the total number of bricks and the length of mortar required for a wall with specific dimensions and features. --- ## **Given Data:** - **Total length of wall:** 80 ft - **Height of each brick:** 8 inches (which is **2/3 ft**) - **Overhead door width:** 12 ft - **Height of overhead door:** 8 ft - **Number of rows of bricks:** 5 - **Mortar joint thickness:** 0.8 inches (which is **2/15 ft**) --- ## **Step 1: Calculate Effective Wall Length** ### Wall Length Excluding Door \[ \text{Remaining Length} = \text{Total Length} - \text{Door Width} = 80\, ft - 12\, ft = 68\, ft \] --- ## **Step 2: Calculate Total Height of Wall** ### Total Height of Wall - The total height of the wall is given as **17 ft 4 in**, which converts to: \[ 17\, ft + \frac{4}{12}\, ft = 17 + \frac{1}{3}\, ft = 17.333\, ft \] ### Height of Bricks and Mortar - Each brick height = 8 inches = \( \frac{2}{3}\, ft \) - Total height for 5 rows of bricks: \[ \text{Total Height of Bricks} = 5 \times \frac{2}{3}\, ft = \frac{10}{3}\, ft \approx 3.333\, ft \] The remaining height must be accounted for mortar joints and structural elements. --- ## **Step 3: Determine the Number of Bricks per Row** ### Brick Length Calculation Assuming a standard brick length of **8 inches**, with a mortar joint of **0.8 inches** between each brick: \[ \text{Length of one brick with mortar} = 8\, in + 0.8\, in = 8.8\, in = \frac{8.8}{12}\, ft \approx 0.733\, ft \] ### Calculate Number of Bricks in a Row Number of bricks per row can be calculated as follows: \[ \text{Number of Bricks per Row} = \frac{\text{Remaining Length}}{\text{Length of one brick with mortar}} = \frac{68\, ft}{0.733\, ft} \approx 92.7 \approx 92 \text{ (rounding down)} \] --- ## **Step 4: Total Number of Bricks** ### Total Bricks for 5 Rows \[ \text{Total Number of Bricks} = \text{Bricks per Row} \times \text{Number of Rows} = 92 \times 5 = 460 \] --- ## **Step 5: Calculate Mortar Joints** ### Mortar Joints in Each Row - Each row has \( \text{Bricks per Row} - 1 \) joints: \[ \text{Mortar Joints per Row} = 92 - 1 = 91 \] ### Total Mortar Joints for 5 Rows \[ \text{Total Mortar Joints} = 91 \times 5 = 455 \] --- ## **Step 6: Calculate Total Length of Mortar** ### Total Length of Mortar The total length of mortar required is: \[ \text{Total Length of Mortar} = \text{Total Mortar Joints} \times \text{Mortar Joint Thickness} \] Convert thickness to feet: \[ \text{Total Length of Mortar} = 455 \times \frac{0.8\, in}{12} = 455 \times \frac{2}{15} \approx 60.67\, ft \] --- ## **Final Answer:** ### Summary - **Total Number of Bricks:** 460 - **Total Length of Mortar:** Approximately **60.67 ft** This structured approach provides a clear calculation method based on the given information and standard assumptions.