Answer:
Part A: There are 18 rows of bricks are needed
Part B: The height of the wall is 5 feet and 3/8 inches (60.375 inches)
Step-by-step explanation:
* Lets explain how to solve the problem
- A mason will lay rows of bricks to build a wall
- The mason will spread 3/8" of mortar on top of all but the last row
of bricks
- The height of the wall = (height of one bricks + the height of the
mortar) × (number of rows of bricks - last brick) + the height of the
last brick
- The dimensions of each brick are 8 × 3 × 2 1/4 inches
- The height if the wall is 1 1/8 inches less than 4
∵ 1 foot =12 inches
∴ The height of the wall = 4 × 12 - 1 1/8 = 46.875 ⇒ (1)
Part A:
∵ The height of the mortar is 3/8 inch
∵ The mason wants to lay the bricks so that the shortest edge of
each brick is vertical
∵ The shortest edge is 2 1/4 inches
- Assume that the number of rows of bricks in the wall is n
∴ The height of the wall = (2 1/4 + 3/8)(n - 1) + 2 1/4
∴ The height of the wall = 2.625(n - 1) + 2 1/4 ⇒ (2)
- Equate (1) and (2)
∴ 2.625(n - 1) + 2 1/4 = 46.875
- Subtract 2 1/4 from both sides
∴ 2.625(n - 1) = 44.625
- Divide both sides by 2.625
∴ n - 1 = 17
- Add 1 to both sides
∴ n = 18
∴ There are 18 rows of bricks are needed
Part B:
- The mason decides to lay bricks so that the 3-inch edge is vertical
∴ The height of the bricks is 3 inches
- The mason lays the same number of rows of bricks that were used
for the wall described in Part A
∴ The number of rows is 18
- The height of the wall = (height of one bricks + the height of the
mortar) × (number of rows of bricks - last brick) + the height of the
last brick
∴ The height of the wall = (3 + 3/8) (18 - 1) + 3
∴ The height of the wall = (3.375 × 17) + 3 = 60.375 inches
∴ The height of the wall is 60.375 inches
∵ 1 inch = 1/12 foot
∴ The height of the wall = 5 1/32 feet
∵ 1/32 feet = 1/32 × 12 = 3/8
∴ The height of the wall is 5 feet and 3/8 inches
