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How Much for a New Floor?

Mr. Coleman has just moved into his new home. He doesn't like the old carpets, so he decides to put laminate flooring throughout the whole ground floor.

The laminate flooring he has chosen comes in packs which each cover [tex]$2 \text{ m}^2$[/tex].
Each room also needs a trim around the perimeter of the room.
The trim comes in packs which have a total length of [tex]$4 \text{ m}$[/tex].

Help Mr. Coleman calculate the floor area of each room and the trim needed for every room, then work out how much it will cost.

\begin{tabular}{|c|l|l|}
\hline
\textbf{Beech Wood} & \textbf{Floor area} [tex]$\left(\text{m}^2\right)$[/tex] & \textbf{Trim} [tex]$\left(\text{m}\right)$[/tex] \\
\hline
Hall & 40 & 30 \\
\hline
Toilet & 30 & 25 \\
\hline
Total & & \\
\hline
& & \\
\hline
\textbf{Oak Wood} & \textbf{Floor area} [tex]$\left(\text{m}^2\right)$[/tex] & \textbf{Trim} [tex]$\left(\text{m}\right)$[/tex] \\
\hline
Living Room & & \\
\hline
Kitchen & & \\
\hline
Office & & \\
\hline
Conservatory & & \\
\hline
Total & & \\
\hline
\end{tabular}

The hall and toilet are to have beech flooring and the other rooms will have oak.

\begin{tabular}{|l|c|c|c|}
\hline
& \begin{tabular}{c}
Number of \\
Packs \\
Needed
\end{tabular} & \begin{tabular}{c}
Price per \\
Pack
\end{tabular} & \textbf{Total Cost} \\
\hline
\begin{tabular}{c}
Beech wood \\
Flooring
\end{tabular} & & [tex]$\$[/tex] 14.99[tex]$ & \\
\hline
\begin{tabular}{c}
Beech wood \\
Trim
\end{tabular} & & $[/tex]\[tex]$ 4.99$[/tex] & \\
\hline
\end{tabular}



Answer :

GinnyAnswer
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.

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