Ask a New Question
Menu

Question content area top

Part 1
A mason will lay rows of bricks to build a wall. The mason will spread three eighths
inch of mortar on top of all but the last row of bricks. The finished wall will be 1 and one eighth
inches less than 4 feet high. Answer parts a and b below.
Question content area bottom
Part 1
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.
Let b equal the number of rows of bricks. The total height of the bricks in inches is equal to
▼
times
▼
b plus 1.
b minus 1.
b.
The total height of the mortar is equal to
▼
three eighths
2 and one fourth
8
3
times
▼
b.
b minus 1.
b plus 1.
Their sum is equal to the height of the wall or
  
enter your response here inches. If I write this as an equation and solve for​ b, then the result is
  
enter your response here rows of bricks.
​(Simplify your​ answers.)

1 answer

To solve this problem, let's break it down step by step.

The finished wall height needs to be given in inches since we are dealing with heights that involve inches.

  1. Convert the height of the wall to inches: Since the finished wall will be \(1 \frac{1}{8}\) inches less than 4 feet, first convert 4 feet into inches.

    4 feet = 4 × 12 inches = 48 inches.
    Therefore, the height of the wall = \(48 - 1 \frac{1}{8}\) inches = \(48 - 1.125\) inches = \(46.875\) inches.

  2. Define the dimensions: Let's say the height of each brick is \(h\) inches. When the mason lays the bricks, mortar is only spread on top of all but the last row.

  3. Total height of bricks: The total height of the bricks if there are \(b\) rows would be: \[ \text{Height of bricks} = h \times b \]

  4. Total height of mortar: Since mortar is spread on all but the last row, we have \(b-1\) spaces between rows to account for. Therefore, the total height of the mortar would be: \[ \text{Height of mortar} = \frac{3}{8} \text{ inches} \times (b - 1) \]

  5. Set up the equation: The sum of the total height of the bricks and the total height of the mortar needs to equal the height of the wall: \[ h \cdot b + \frac{3}{8} \cdot (b - 1) = 46.875 \]

    We want to express everything in terms of \(b\). Assuming you know the height of each brick (let's denote it as \(h\)), we can solve for \(b\).

  6. Example brick height: If we assume each brick has a height of 2.5 inches (you may adjust this based on the actual brick height), we substitute \(h = 2.5\) into the equation: \[ 2.5b + \frac{3}{8}(b - 1) = 46.875 \]

    This simplifies to: \[ 2.5b + \frac{3}{8}b - \frac{3}{8} = 46.875 \]

    Multiply everything through by 8 to eliminate the fraction: \[ 20b + 3b - 3 = 375 \]

    Combine like terms: \[ 23b - 3 = 375 \]

    Add 3 to both sides: \[ 23b = 378 \]

    Divide by 23: \[ b = \frac{378}{23} \approx 16.43 \]

    Since \(b\) must be a whole number, round up if it's not a whole number. Thus, you would need 17 rows of bricks.

If you have a different brick height, plug it into \(h\) and follow similarly to find \(b\).