Let's break down the tasks for Part 1 of Xavier's house construction project.
### Part 1: The Math Behind Construction
1. **Calculate the Total Area of Xavier’s Lot:**
Since the shape of the lot is a trapezoid, we use the formula for the area of a trapezoid:
\[
A = \frac{(a + b)}{2} \times c
\]
Where:
- \(a\) = Front of the lot (unknown, but let's assume it's \(x\) feet for now)
- \(b\) = Back of the lot = 100 feet
- \(c\) = Length of the lot (unknown, but let's assume it's \(y\) feet for now)
Since we don't know \(a\) and \(c\), we'll leave this as a variable equation for the moment.
**Total Area of Lot = \( \frac{(a + 100)}{2} \times c\)**
2. **Calculate the Available Lot Coverage:**
The county allows 40% of the total area for buildings.
\[
\text{Available Lot Coverage} = \frac{40}{100} \times \text{Total Area}
\]
3. **Calculate the Total Price for Option 1:**
For Option 1, the total square footage is 1,811 sq ft at $180 per square foot:
\[
\text{Total Price for Option 1} = 1,811 \times 180
\]
\[
= 326,000
\]
4. **Calculate the Total Price for Option 2:**
For Option 2, the total square footage is 2,600 sq ft at $195 per square foot:
\[
\text{Total Price for Option 2} = 2,600 \times 195
\]
\[
= 507,000
\]
5. **Calculate Transportation Costs:**
The transportation cost for each module is given by the formula:
\[
\text{Cost} = [(.20 \times 350) + 500] \times \text{Number of Modules}
\]
For Option 1 (4 modules) and Option 2 (5 modules):
\[
\text{Transportation Cost (Option 1)} = [(.20 \times 350) + 500] \times 4
\]
\[
= [70 + 500] \times 4 = 570 \times 4 = 2,280
\]
\[
\text{Transportation Cost (Option 2)} = [(.20 \times 350) + 500] \times 5
\]
\[
= [70 + 500] \times 5 = 570 \times 5 = 2,850
\]
### Summary of Calculated Values:
1. **Total Area of Lot:** (Requires dimensions of \(a\) and \(c\))
2. **Available Lot Coverage:** 40% of Total Area
3. **Total Price for Option 1:** $326,000
4. **Total Price for Option 2:** $507,000
5. **Transportation Cost for Option 1:** $2,280
6. **Transportation Cost for Option 2:** $2,850
---
### Part 2: Job Board Creation
For your job board, here's what to include based on the calculations above:
1. **Rough Drawing of Xavier’s Lot:**
- Sketch a trapezoidal lot.
- Include a label for the total area, once calculated.
2. **Sketch of Prefabricated House Option:**
- If you suggest Option 1, include a rough floor plan for the 1,811 sq ft house.
- Label the final cost of $326,000.
- Highlight features like upgraded PEX piping and fiber cement siding.
3. **Transportation Truck Graphic:**
- Include an image of a truck (e.g., clip art).
- Write the transportation cost of $2,280 for Option 1 or $2,850 for Option 2 next to it.
### Example Layout:
- Top of the board: Title ("Xavier's House Construction Project")
- Left side: Drawing of the lot with dimensions
- Center: Drawing of the prefab house with amenities labeled
- Right side: Truck graphic with transportation costs
Remember to make your job board colorful and organized to make it clear and visually appealing for Xavier. Good luck with your project!