5. performance task a mason will lay rows of
bricks to build a wall. the mason will spread
inch of mortar on top of all but the last row
of bricks. the finished wall will be 1 inch less
than 4 feet high.
8 in.
ool w
3 in.
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 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)