Let's help Mr. Coleman calculate the total cost for installing Beech wood flooring and trim for his new house. Here's a step-by-step solution detailing the calculations for each part of the problem:
### Step 1: Calculate the Total Floor Area
We need to add the floor area for the Hall and the Toilet:
- Hall: [tex]\(4,000,000 \, \text{m}^2\)[/tex]
- Toilet: [tex]\(3,000,000 \, \text{m}^2\)[/tex]
The total floor area is:
[tex]\[
4,000,000 \, \text{m}^2 + 3,000,000 \, \text{m}^2 = 7,000,000 \, \text{m}^2
\][/tex]
### Step 2: Calculate the Total Trim Length
Next, we sum up the trim lengths needed for the Hall and the Toilet:
- Hall: [tex]\(3,000 \, \text{m}\)[/tex]
- Toilet: [tex]\(2,500 \, \text{m}\)[/tex]
The total trim length is:
[tex]\[
3,000 \, \text{m} + 2,500 \, \text{m} = 5,500 \, \text{m}
\][/tex]
### Step 3: Determine Number of Packs Needed
We know that:
- Each pack of flooring covers [tex]\(2 \, \text{m}^2\)[/tex].
- Each pack of trim covers [tex]\(4 \, \text{m}\)[/tex].
For flooring:
[tex]\[
\text{Total packs needed} = \frac{7,000,000 \, \text{m}^2}{2 \, \text{m}^2/\text{pack}} = 3,500,000 \, \text{packs}
\][/tex]
For trim:
[tex]\[
\text{Total packs needed} = \frac{5,500 \, \text{m}}{4 \, \text{m}/\text{pack}} = 1,375 \, \text{packs}
\][/tex]
### Step 4: Calculate the Cost
We know the prices per pack:
- Beech wood flooring: [tex]$\$[/tex]14.99[tex]$ per pack.
- Beech wood trim: $[/tex]\[tex]$4.99$[/tex] per pack.
Total cost for Beech wood flooring:
[tex]\[
3,500,000 \, \text{packs} \times \$14.99/\text{pack} = \$52,465,000.00
\][/tex]
Total cost for Beech wood trim:
[tex]\[
1,375 \, \text{packs} \times \$4.99/\text{pack} = \$6,861.25
\][/tex]
### Summary
[tex]\[
\begin{array}{|c|c|c|}
\hline
\text{Beech Wood} & \text{Total Area (m}^2\text{)} & \text{Total Trim (m)} \\
\hline
\text{Hall} & 4,000,000 & 3,000 \\
\hline
\text{Toilet} & 3,000,000 & 2,500 \\
\hline
\text{Total} & 7,000,000 & 5,500 \\
\hline
\end{array}
\][/tex]
[tex]\[
\begin{array}{|c|c|c|c|}
\hline
& \text{Number of Packs Needed} & \text{Price per Pack} & \text{Total Cost} \\
\hline
\text{Beech wood Flooring} & 3,500,000 & \$14.99 & \$52,465,000.00 \\
\hline
\text{Beech wood Trim} & 1,375 & \$4.99 & \$6,861.25 \\
\hline
\end{array}
\][/tex]
Thus, the total cost for Beech wood flooring and trim is \$52,471,861.25.
