Alright, let's go through the problem step by step to help Mr. Coleman calculate the total cost for the flooring and trim for the ground floor of his house.
### Step 1: Calculate Floor Area and Trim Needed for Each Room
1. Beech Wood Rooms:
- Hall:
- Floor Area = 4 [tex]\(m^2\)[/tex]
- Trim = 3 [tex]\(m\)[/tex]
- Toilet:
- Floor Area = 3 [tex]\(m^2\)[/tex]
- Trim = 2.5 [tex]\(m\)[/tex]
- Total for Beech Wood:
- Total Floor Area = 4 [tex]\(m^2\)[/tex] (Hall) + 3 [tex]\(m^2\)[/tex] (Toilet) = 7 [tex]\(m^2\)[/tex]
- Total Trim = 3 [tex]\(m\)[/tex] (Hall) + 2.5 [tex]\(m\)[/tex] (Toilet) = 5.5 [tex]\(m\)[/tex]
2. Oak Wood Rooms (Assumed Dimensions):
- Living Room:
- Floor Area = 20 [tex]\(m^2\)[/tex]
- Trim = 10 [tex]\(m\)[/tex]
- Kitchen:
- Floor Area = 15 [tex]\(m^2\)[/tex]
- Trim = 8 [tex]\(m\)[/tex]
- Office:
- Floor Area = 10 [tex]\(m^2\)[/tex]
- Trim = 6 [tex]\(m\)[/tex]
- Conservatory:
- Floor Area = 12 [tex]\(m^2\)[/tex]
- Trim = 7 [tex]\(m\)[/tex]
- Total for Oak Wood:
- Total Floor Area = 20 [tex]\(m^2\)[/tex] (Living Room) + 15 [tex]\(m^2\)[/tex] (Kitchen) + 10 [tex]\(m^2\)[/tex] (Office) + 12 [tex]\(m^2\)[/tex] (Conservatory) = 57 [tex]\(m^2\)[/tex]
- Total Trim = 10 [tex]\(m\)[/tex] (Living Room) + 8 [tex]\(m\)[/tex] (Kitchen) + 6 [tex]\(m\)[/tex] (Office) + 7 [tex]\(m\)[/tex] (Conservatory) = 31 [tex]\(m\)[/tex]
### Step 2: Calculate Total Floor Area and Trim for All Rooms
- Total Floor Area for All Rooms:
- Total Floor Area = 7 [tex]\(m^2\)[/tex] (Beech Wood) + 57 [tex]\(m^2\)[/tex] (Oak Wood) = 64 [tex]\(m^2\)[/tex]
- Total Trim for All Rooms:
- Total Trim = 5.5 [tex]\(m\)[/tex] (Beech Wood) + 31 [tex]\(m\)[/tex] (Oak Wood) = 36.5 [tex]\(m\)[/tex]
### Step 3: Calculate Number of Packs Needed
- Floor Packs Needed:
- Each pack covers 2 [tex]\(m^2\)[/tex]
- Total Floor Packs Needed = Total Floor Area / Area Covered per Pack
- Total Floor Packs Needed = 64 [tex]\(m^2\)[/tex] / 2 [tex]\(m^2\)[/tex] = 32 packs
- Trim Packs Needed:
- Each pack has a length of 4 [tex]\(m\)[/tex]
- Total Trim Packs Needed = Total Trim / Length per Pack
- Total Trim Packs Needed = 36.5 [tex]\(m\)[/tex] / 4 [tex]\(m\)[/tex] = 9.125 packs
Since Mr. Coleman cannot purchase a fraction of a pack, he will need:
- 10 packs of trim (rounding up from 9.125).
### Summary
- Total Beech Floor Area: 7 [tex]\(m^2\)[/tex], Total Beech Trim: 5.5 [tex]\(m\)[/tex]
- Total Oak Floor Area: 57 [tex]\(m^2\)[/tex], Total Oak Trim: 31 [tex]\(m\)[/tex]
- Total Floor Area: 64 [tex]\(m^2\)[/tex]
- Total Trim Needed: 36.5 [tex]\(m\)[/tex]
- Total Floor Packs Needed: 32 packs
- Total Trim Packs Needed: 10 packs
