Respuesta :
Answer:
Part A: There are 18 rows of bricks are needed
Part B: The height of the wall is 5 1/32 feet (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 dimensions of each brick are 8 inches , 3 inches , 2 1/4 inches
- The mason will spread 3/8 inch of mortar on top of all but the last
row of bricks
- The finished wall will be 1 1/8 inch less than 4 feet high
# Part A:
- The mason wants to lay the bricks so that the shortest edge of each
brick is vertical.
- We need to find how many rows of bricks are needed
* At first lets change the height of the wall to inch
∵ 1 foot = 12 inches
∴ 4 feet = 4 × 12 = 48 inches
∵ The height of the wall is 1 1/8 inch less than 4
∴ The height of the wall = 48 - 1 1/8 = 46.875 inches
- Assume that the number of rows is n
∵ The shortest edge of the brick is 2 1/4 inch
∵ The mason will spread 3/8 inch of mortar on top of all but the last
row of bricks
∴ The height of each bricks with mortar = 2 1/4 + 3/8 = 2.625 inches
∵ All the rows have mortar on the top except the last row
∵ The number of rows are n
∴ The number of rows with mortar is (n - 1)
∴ The height of the wall = 2.625 (n - 1) + 2 1/4
∵ The height of the wall is 46.875 inches
∴ 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 for both sides
∴ n = 18
∵ n represents the number of rows
∴ 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 mason lays the same number of rows of bricks that were used
for the wall described in Part A
- We need to find how high will this wall be
∵ There are 18 row in Part A
∵ The height of the bricks is the edge of 3 inches
∵ There is 3/8 mortar over the top of each row except the last one
∴ The height of each row except the last one = 3 + 3/8 = 3.375 in.
∵ The height of the last row = 3 inches
∴ The height of the wall = 17 × 3.375 + 3 = 60.375 inches
∵ 1 inch = 1/12 feet
∴ The height of the wall = 60.375 × 1/12 = 5 1/32 feet
∴ The height of the wall is 5 1/32 feet (60.375 inches)
Answer:
Part A: There are 18 rows of bricks are needed.
Part B: The height of the wall is 5 1/32 feet.
