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 finished wall will be 1 1/8" less than 4 feet high.

Part A The mason wants to lay the bricks so that the shortest edge of each brick is vertical. How many rows of bricks are needed? Show your work.

Part B Suppose the mason decides to lay bricks so that the 3-inch edge is vertical. If the mason lays the same number of rows of bricks that were used for the wall described in Part A, how high will this wall be?

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