Question

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
3
times
▼
The total height of the mortar is equal to
▼
three eighths
2 and one fourth
3
8
times
▼
b.
b plus 1.
b minus 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.

Answer 1

To solve this problem, we need to first establish a few quantities based on the given information.

### Step 1: Convert the height of the wall to inches
The finished wall will be \( 4 \text{ feet} - 1 \frac{1}{8} \text{ inches} \).

1. Convert 4 feet to inches:
\[
4 \text{ ft} = 4 \times 12 = 48 \text{ inches}
\]

2. Convert \( 1 \frac{1}{8} \) inches to a decimal:
\[
1 + \frac{1}{8} = \frac{8}{8} + \frac{1}{8} = \frac{9}{8} \text{ inches} = 1.125 \text{ inches}
\]

3. Calculate the total height of the wall in inches:
\[
\text{Total height} = 48 - 1.125 = 46.875 \text{ inches}
\]

### Step 2: Set up the equation for the height
Let \( b \) be the number of rows of bricks.

1. The total height of the bricks in inches is given by the height of each brick multiplied by the number of rows. Assuming the height of each brick is \( 3 \) inches:
\[
\text{Total height of bricks} = 3b \text{ inches}
\]

2. The total height of the mortar is \( \frac{3}{8} \) inches spread on top of all but the last row of bricks, which means it will be applied to \( b-1 \) rows:
\[
\text{Total height of mortar} = \frac{3}{8} (b - 1) \text{ inches}
\]

### Step 3: Combine the heights
The sum of the height of the bricks and the height of the mortar equals the total height of the wall:
\[
3b + \frac{3}{8}(b - 1) = 46.875
\]

### Step 4: Solve for \( b \)
1. Clear the fraction by calculating \( \frac{3}{8} \times (b - 1) \):
\[
\frac{3}{8}b - \frac{3}{8}
\]

2. Substitute this back into the equation:
\[
3b + \frac{3}{8}b - \frac{3}{8} = 46.875
\]

3. To eliminate the fraction, multiply the entire equation by 8:
\[
24b + 3b - 3 = 375
\]
\[
27b - 3 = 375
\]
\[
27b = 378
\]
\[
b = \frac{378}{27} = 14
\]

### Final Answer
The number of rows of bricks needed is \( b = 14 \).

### Summary
- The total height of the wall in inches is \( 46.875 \).
- The required number of rows of bricks is \( 14 \).