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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 house.

The laminate flooring he has chosen comes in packs which each cover [tex]2 \, 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 4 meters.

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.

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

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

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



Answer :

GinnyAnswer
### Beech Wood

#### Floor Areas and Trim Lengths
- Hall:
- Floor area: [tex]\( 4,000,000 \, m^2 \)[/tex]
- Trim length: [tex]\( 300 \, m \)[/tex]

- Toilet:
- Floor area: [tex]\( 30 \, m^2 \)[/tex]
- Trim length: [tex]\( 14 \, m \)[/tex]

- Total for Beech Wood:
- Floor area: [tex]\( 4,000,000 \, m^2 + 30 \, m^2 = 4,000,030 \, m^2 \)[/tex]
- Trim length: [tex]\( 300 \, m + 14 \, m = 314 \, m \)[/tex]

#### Cost Calculation for Beech Wood

1. Flooring:
- Packs needed: [tex]\( \frac{4,000,030 \, m^2}{2 \, m^2/\text{pack}} = 2,000,015 \, \text{packs} \)[/tex]
- Price per pack: \[tex]$14.99 - Total cost: \( 2,000,015 \, \text{packs} \times \$[/tex]14.99 = \[tex]$29,980,224.85 \) 2. Trim: - Packs needed: \( \frac{314 \, m}{4 \, m/\text{pack}} = 79 \, \text{packs} \) - Price per pack: \$[/tex]4.99
- Total cost: [tex]\( 79 \, \text{packs} \times \$4.99 = \$394.21 \)[/tex]

3. Grand Total for Beech Wood:
- [tex]\( \$29,980,224.85 + \$394.21 = \$29,980,619.06 \)[/tex]


### Oak Wood

#### Floor Areas and Trim Lengths
- Living Room:
- Floor area: [tex]\( 40 \, m^2 \)[/tex]
- Trim length: [tex]\( 26 \, m \)[/tex]

- Kitchen:
- Floor area: [tex]\( 25 \, m^2 \)[/tex]
- Trim length: [tex]\( 18 \, m \)[/tex]

- Office:
- Floor area: [tex]\( 20 \, m^2 \)[/tex]
- Trim length: [tex]\( 16 \, m \)[/tex]

- Conservatory:
- Floor area: [tex]\( 30 \, m^2 \)[/tex]
- Trim length: [tex]\( 22 \, m \)[/tex]

- Total for Oak Wood:
- Floor area: [tex]\( 40 \, m^2 + 25 \, m^2 + 20 \, m^2 + 30 \, m^2 = 115 \, m^2 \)[/tex]
- Trim length: [tex]\( 26 \, m + 18 \, m + 16 \, m + 22 \, m = 82 \, m \)[/tex]

#### Cost Calculation for Oak Wood

1. Flooring:
- Packs needed: [tex]\( \frac{115 \, m^2}{2 \, m^2/\text{pack}} = 58 \, \text{packs} \)[/tex]
- Price per pack: \[tex]$18.99 - Total cost: \( 58 \, \text{packs} \times \$[/tex]18.99 = \[tex]$1,101.42 \) 2. Trim: - Packs needed: \( \frac{82 \, m}{4 \, m/\text{pack}} = 21 \, \text{packs} \) - Price per pack: \$[/tex]5.99
- Total cost: [tex]\( 21 \, \text{packs} \times \$5.99 = \$125.79 \)[/tex]

3. Grand Total for Oak Wood:
- [tex]\( \$1,101.42 + \$125.79 = \$1,227.21 \)[/tex]

### Summary
Mr. Coleman's total cost for flooring and trimming his new home's rooms with laminate flooring is:
- Beech Wood Total Cost: \[tex]$29,980,619.06 - Oak Wood Total Cost: \$[/tex]1,227.21

Overall Grand Total: [tex]\( \$29,980,619.06 + \$1,227.21 = \$29,981,846.27 \)[/tex]

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