Let's go through problem step-by-step. --- ## **Step 1: Understand the problem** - The wall is 80 ft long. - The wall consists of **8-inch-high** and **16-inch-long** bricks. - The **overhead doors** are 12 ft wide. - Mortar joints are .8 in thick. - The goal: To find **how many bricks (or blocks)** are needed to complete the wall. --- ## **Step 2: Convert all measurements consistent units** ### Wall length: - 80 ft = \( 80 \times 12 = 960 \) inches ### Brick dimensions: - Height: 8 inches - Length: 16 inches ### Mortar joint: - .8 inches ### Overhead door width: - 12 ft = \( 12 \times 12 = 144 \) inches --- ## **Step 3: Calculate the number of bricks along the length** **Number of bricks along length**: \[ \text{Bricks per row} = \frac{\text{Total wall length}}{\text{Brick length} + \text{Mortar joint}} \] But because mortar joints are between bricks, each brick's *effective length* including mortar is: \[ 16\, \text{in} + .8\, \text{in} = 16.8\, \text{in} \] Number of bricks: \[ \frac{960\, \text{in}}{16.8\, \text{in}} \approx 57.14 \] Since we need whole bricks, **round down to 57 bricks per row** (assuming no partial bricks). --- ## **Step 4: Calculate the number of courses (rows)** - Total height of the wall: \[ \text{Total height} = 17\, \text{ft} - 4\, \text{ft} = 13\, \text{ft} \] Convert to inches: \[ 13\, \text{ft} \times 12 = 156\, \text{in} \] - Brick height + mortar: \[ 8\, \text{in} + .8\, \text{in} = 8.8\, \text{in} \] Number of courses: \[ \frac{156\, \text{in}}{8.8\, \text{in}} \approx 17.73 \] Round down to 17 courses. --- ## **Step 5: Calculate total bricks** - Total bricks without considering doors: \[ \text{Total bricks} = \text{Number of bricks per row} \times \text{Number of rows} \] \[ = 57 \times 17 = 969 \] --- ## **Step 6: Adjust for the doors** - The door spans 144 inches (12 ft). - The door replaces a segment of bricks in one or more rows. ### How many bricks does the door cover? - Each brick (including mortar): \[ 16.8\, \text{in} \] - Bricks needed to cover 144 inches: \[ \frac{144\, \text{in}}{16.8\, \text{in}} \approx 8.57 \] - So, approximately 8 or 9 bricks per row are replaced by the door. ### Number of rows the door spans: - **Assuming** the door is centered and spans the full height of the wall, it affects all 17 rows. - Total bricks replaced: \[ 8 \text{ bricks per row} \times 17 \text{ rows} = 136 \] --- ## **Step 7: Final total bricks needed** - Total bricks without considering the door: \[ 969 \] - Subtract bricks replaced by the door: \[ 969 - 136 = 833 \] --- ## **## Final Answer:** **Approximately \(\boxed{833}\) bricks are required to complete the wall.** --- **Note:** Small variations may occur depending on exact brick placement and mortar allowances, but this provides a solid estimate based on provided dimensions.