Let's go through the problem step-by-step: --- ## **Step 1: Understand the problem** - The wall height is 8 inches. - The wall is 80 feet long. - The wall is made of bricks/blocks of two types: - 8-inch-high bricks - 16-inch-high bricks - The wall is built with vertical courses of bricks (rows). - The total height of the wall is 8 inches (which is the height of one course). - The total length of the wall is 80 feet. - Overhead doors are 12 feet wide and are to be incorporated into the wall. - Mortar joints are .8 inches thick. - Goal: Determine the **quantity of 8-inch-high and 16-inch-high bricks/blocks** required to complete the wall. --- ## **Step 2: Convert all measurements to consistent units** - Wall length: 80 feet = \( 80 \times 12 = 960 \) inches - Overhead doors: 12 feet wide = \( 12 \times 12 = 144 \) inches - Wall height: 8 inches (already in inches) - Mortar joints: .8 inches thick (per joint) --- ## **Step 3: Determine the number of courses (rows)** Since the wall height is 8 inches, and each course is 8 inches high, the wall consists of **1 course** of bricks. --- ## **Step 4: Determine the number of bricks per course** - **Total length of wall:** 960 inches - **Subtract the width of the door(s):** Since the figure shows 3 doors, each 12 ft (144 inches), total door width: \( 3 \times 144 = 432 \) inches - **Remaining length of wall (excluding doors):** \( 960 - 432 = 528 \) inches - **Number of bricks in each section:** Each brick is 8 inches long, but mortar joints of .8 inches are between bricks. - Effective length of each brick including joint: \( 8 + .8 = 8.8 \) inches - **Number of bricks per wall (excluding doors):** \( \frac{528}{8.8} \approx 60 \) bricks - **Total bricks needed:** Since the door openings are cut out, and the total length of bricks (excluding doors) is 528 inches, the total number of bricks: \( \boxed{60 \text{ bricks per course}} \) --- ## **Step 5: Determine quantity of bricks** - The wall has **1 course**, so: \[ \text{Total bricks} = 60 \] - However, the wall includes **both 8-inch-high bricks** and **16-inch-high bricks**. --- ## **Step 6: Determine the arrangement of bricks** From the figure, the wall has alternating brick sizes in different sections, with the following observations: - The wall sections are built with **rows of bricks** of **8 inches height** and **16 inches height**. - The wall height is 8 inches, so: - **8-inch-high bricks** are used in **single courses**. - **16-inch-high bricks** are used in **double courses** (stacked vertically). **But**, since the total wall height is 8 inches, it indicates: - Only **8-inch-high bricks** are used for the entire wall. **Alternatively**, if the figure shows a pattern of sections with 8-inch and 16-inch bricks, perhaps the wall height is made up of **multiple courses**. --- ## **Step 7: Clarify the brick arrangement** Given the description, the wall is 8 inches high, and the figure shows: - Some sections with **single bricks** (8-inch high), - Some sections with **stacked bricks** (two bricks of 8-inch height each). Thus, **the wall is built with a combination of:** - **Single courses** of 8-inch-high bricks, - **Double courses** of 8-inch-high bricks stacked to form 16-inch-high sections. But the total height is 8 inches, so: - **All bricks are 8 inches high**, or - **Double courses** are stacked to reach 16 inches (but that exceeds total height). **Conclusion:** - The wall is 8 inches high, so **only 8-inch-high bricks** are used. --- ## **Step 8: Final calculation of bricks** ### **Number of bricks** - **Total length excluding doors:** 528 inches - **Brick length including mortar joint:** 8.8 inches - **Number of bricks:** \[ \frac{528}{8.8} \approx 60 \] ### **Answer:** - **Number of 8-inch-high bricks needed:** **60** --- ## **Final answer:** \[ \boxed{ \text{Number of 8-inch-high bricks} = 60 } \] **Note:** The problem states "8-inch-high by 16-inch-long bricks," so all bricks are 8 inches high and 16 inches long. The calculation confirms 60 bricks are needed for the length of the wall, excluding the doors. The total quantity of bricks is **60**. --- **If the question asks for quantities of both types of bricks (8-inch-high and 16-inch-long), then:** - **Number of bricks:** 60 - **Type of bricks:** - All are 8 inches high (since the wall height is 8 inches). - Length of each brick: 16 inches (including joints). --- **Summary:** | Aspect | Calculation / Note | |---------|---------------------| | Total length of wall | 960 inches | | Total door width | 432 inches | | Remaining length | 528 inches | | Effective brick length | 8.8 inches (including mortar) | | Number of bricks | 60 bricks | **Therefore, 60 bricks of 8 inches high and 16 inches long are required.**