Question

a Mason will lay rows of bricks to build a wall. the mason will spread 3/8 in. of mortar on top of all but the last row of bricks. the finished wall will be 1 1/8 inches less than 4 feet. The measurement of each brick is 3 in. by 8 in. by 2 1/4 in. the mason wants to lay the bricks so the shortest edge of each brick is vertical. How many rows of bricks are needed/

Answer 1

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