Answer :
Mr. Coleman wants to replace the old carpets in the hall and toilet with beech laminate flooring and needs a trim around the perimeter of these rooms. Let's calculate the total floor area and trim required, along with the total cost.
### Step-by-Step Solution:
#### 1. Calculate the Total Floor Area for Beech Wood
- Hall Floor Area: 4,000,000 m²
- Toilet Floor Area: 3,000,600 m²
Total Beech Floor Area:
[tex]\[ \text{Total Beech Floor Area} = 4,000,000 \, \text{m}^2 + 3,000,600 \, \text{m}^2 = 7,000,600 \, \text{m}^2 \][/tex]
#### 2. Calculate the Total Trim Length for Beech Wood
- Hall Trim Length: 3,000 m
- Toilet Trim Length: 2,500 m
Total Beech Trim Length:
[tex]\[ \text{Total Beech Trim Length} = 3,000 \, \text{m} + 2,500 \, \text{m} = 5,500 \, \text{m} \][/tex]
#### 3. Calculate Number of Packs Needed for Flooring and Trim
Each pack of beech flooring covers 2 m² and each pack of trim covers 4 m.
Packs of Beech Flooring Needed:
[tex]\[ \text{Beech Flooring Packs Needed} = \left\lceil \frac{7,000,600 \, \text{m}^2}{2 \, \text{m}^2/\text{pack}} \right\rceil = 3,500,300 \, \text{packs} \][/tex]
Packs of Beech Trim Needed:
[tex]\[ \text{Beech Trim Packs Needed} = \left\lceil \frac{5,500 \, \text{m}}{4 \, \text{m}/\text{pack}} \right\rceil = 1,375 \, \text{packs} \][/tex]
#### 4. Calculate the Cost for Beech Wood Flooring and Trim
- Price per pack of beech flooring: [tex]$14.99 - Price per pack of beech trim: $[/tex]4.99
Total Cost for Beech Flooring:
[tex]\[ \text{Beech Flooring Total Cost} = 3,500,300 \, \text{packs} \times \$14.99/\text{pack} = \$52,469,497.0 \][/tex]
Total Cost for Beech Trim:
[tex]\[ \text{Beech Trim Total Cost} = 1,375 \, \text{packs} \times \$4.99/\text{pack} = \$6,861.25 \][/tex]
### Summary:
- Total Beech Floor Area: 7,000,600 m²
- Total Beech Trim Length: 5,500 m
- Packs of Beech Flooring Needed: 3,500,300 packs
- Packs of Beech Trim Needed: 1,375 packs
- Total Cost for Beech Flooring: \[tex]$52,469,497.0 - Total Cost for Beech Trim: \$[/tex]6,861.25
The total cost for replacing the flooring and trim in the hall and toilet with beech wood is \$52,476,358.25.
### Step-by-Step Solution:
#### 1. Calculate the Total Floor Area for Beech Wood
- Hall Floor Area: 4,000,000 m²
- Toilet Floor Area: 3,000,600 m²
Total Beech Floor Area:
[tex]\[ \text{Total Beech Floor Area} = 4,000,000 \, \text{m}^2 + 3,000,600 \, \text{m}^2 = 7,000,600 \, \text{m}^2 \][/tex]
#### 2. Calculate the Total Trim Length for Beech Wood
- Hall Trim Length: 3,000 m
- Toilet Trim Length: 2,500 m
Total Beech Trim Length:
[tex]\[ \text{Total Beech Trim Length} = 3,000 \, \text{m} + 2,500 \, \text{m} = 5,500 \, \text{m} \][/tex]
#### 3. Calculate Number of Packs Needed for Flooring and Trim
Each pack of beech flooring covers 2 m² and each pack of trim covers 4 m.
Packs of Beech Flooring Needed:
[tex]\[ \text{Beech Flooring Packs Needed} = \left\lceil \frac{7,000,600 \, \text{m}^2}{2 \, \text{m}^2/\text{pack}} \right\rceil = 3,500,300 \, \text{packs} \][/tex]
Packs of Beech Trim Needed:
[tex]\[ \text{Beech Trim Packs Needed} = \left\lceil \frac{5,500 \, \text{m}}{4 \, \text{m}/\text{pack}} \right\rceil = 1,375 \, \text{packs} \][/tex]
#### 4. Calculate the Cost for Beech Wood Flooring and Trim
- Price per pack of beech flooring: [tex]$14.99 - Price per pack of beech trim: $[/tex]4.99
Total Cost for Beech Flooring:
[tex]\[ \text{Beech Flooring Total Cost} = 3,500,300 \, \text{packs} \times \$14.99/\text{pack} = \$52,469,497.0 \][/tex]
Total Cost for Beech Trim:
[tex]\[ \text{Beech Trim Total Cost} = 1,375 \, \text{packs} \times \$4.99/\text{pack} = \$6,861.25 \][/tex]
### Summary:
- Total Beech Floor Area: 7,000,600 m²
- Total Beech Trim Length: 5,500 m
- Packs of Beech Flooring Needed: 3,500,300 packs
- Packs of Beech Trim Needed: 1,375 packs
- Total Cost for Beech Flooring: \[tex]$52,469,497.0 - Total Cost for Beech Trim: \$[/tex]6,861.25
The total cost for replacing the flooring and trim in the hall and toilet with beech wood is \$52,476,358.25.