Maths-
General
Easy

Question

A mason will lay rows of bricks to build a wall. 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.
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 .

hintHint:

1. Height of the wall = (Height of 1 brick row × no. of rows) + (Height of each mortar layer × no. of mortar layers).
2. 1 foot = 12 inches.

The correct answer is: 18 rows of bricks are required to build the given wall



    Step-by-step solution:-
    Let the no. of rows of bricks to be used to build the wall be x.
    ∴ No. of brick rows = x ................................................................................. (Equation i)
    Also, we know that the mortar layer is placed over each brick row except the top row.
    ∴ No. of mortar layers = x - 1 ….................................................................... (Equation ii)
    From the given information, we get-
    Height of the wall = 4 feet - 1 1/8 in.
    ∴ Height of the wall = (4 cross times 12) in. - 9/8 in. ................................................... (1 foot = 12 inches)
    ∴ Height of the wall = 48 - 9/8
    ∴ Height of the wall = (384-9)/8 .................................................................... (Making denominators equal)
    ∴ Height of the wall = 375/8 in. .................................................................... (Equation iii)
    Now, we are given that smallest edge of the brick forms the vertical length of the brick row.
    ∴ Height of 1 brick row = 2 1/4 inches
    ∴ Height of 1 brick row = 9/4 in. ................................................................... (Equation iv)
    Also, height of each mortar layer = 3/8 in. .................................................. (Equation v)

    Final Answer:-
    ∴ 18 rows of bricks are required to build the given wall.

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