3. 2 Tshego also intends tiling the dining room and lounge floors. The dimensions of the lounge floor are 4 m by 5 m and of the dining room floor 3 m by 4 m. Information and cost:... 3. 2 Tshego also intends tiling the dining room and lounge floors. The dimensions of the lounge floor are 4 m by 5 m and of the dining room floor 3 m by 4 m. Information and cost: • Tshego intends using tiles that are 35 cm by 35 cm. • One box of 4 tiles costs R143,84. • Tile cement costs R99,90 per 20 kg bag, which covers 3 m². • She needs 4 bags of tile grout at R89,90 per 5 kg bag. • The cost of labour is R2 500. • Tshego's total budget for the tiling project is R15 000. Use the information above to answer the questions that follow. 3. 2.1 Show that the total floor area to be tiled is 32 m². You may use this formula: Area of a rectangle = length × width (2) 3. 2.2 Determine how many boxes of tiles Tshego will need if an extra 10% of the number of tiles must be added for cutting and breakages. (9) 3. 2.3 Show by means of calculations if Tshego's budget is enough to finish the tiling project. (8) 4. 1 ANNEXURE C shows the seating plan for a cinema during the Covid-19 pandemic. Seats marked with an 'X' need to be left vacant in order to comply with social distancing regulations. Use ANNEXURE C and the information above to answer the questions that follow. 4. 1.1 On which side of the cinema is seat E4 from seat E15 when a person is
Understand the Problem
This is a math problem related to tiling a floor and calculating costs. The user needs to find the area of the floor, the number of tile boxes required (with extra for wastage), and whether the total cost is within budget. The second part of the question involves interpreting a seating plan for a cinema with social distancing measures, and determining relative positions of seats.
Answer
3.2.1: $32 \text{ m}^2$ 3.2.2: 72 boxes 3.2.3: Yes, the budget is enough because the total cost is $R14314.98$ which is less than $R15000$.
Answer for screen readers
3.2.1: $20 \text{ m}^2 + 12 \text{ m}^2 = 32 \text{ m}^2$ 3.2.2: 72 boxes 3.2.3: The total cost is $R14314.98$, which is less than the budget of $R15000$, so the budget is sufficient.
Steps to Solve
3.2.1 Calculate the area of the lounge floor The area of the lounge floor is length $\times$ width $= 4 \text{ m} \times 5 \text{ m} = 20 \text{ m}^2$.
3.2.1 Calculate the area of the dining room floor The area of the dining room floor is length $\times$ width $= 3 \text{ m} \times 4 \text{ m} = 12 \text{ m}^2$.
3.2.1 Calculate the total floor area The total floor area is the sum of the lounge and dining room areas: $20 \text{ m}^2 + 12 \text{ m}^2 = 32 \text{ m}^2$.
3.2.2 Calculate the area of one tile The area of one tile is $35 \text{ cm} \times 35 \text{ cm} = 1225 \text{ cm}^2$. Convert to $\text{m}^2$: $1225 \text{ cm}^2 = 1225 / 10000 \text{ m}^2 = 0.1225 \text{ m}^2$.
3.2.2 Calculate the number of tiles needed without wastage The number of tiles needed is the total area divided by the area of one tile: $32 \text{ m}^2 / 0.1225 \text{ m}^2 \approx 261.22$ tiles
3.2.2 Calculate the extra 10% tiles for wastage Add 10% for cutting and breakages: $261.22 \times 0.10 = 26.122$ tiles.
3.2.2 Calculate the total number of tiles needed The total number of tiles needed is $261.22 + 26.122 = 287.342$ tiles. Since we can't buy fractions of tiles, round up to 288 tiles.
3.2.2 Calculate the number of boxes needed Since there are 4 tiles per box, the number of boxes needed is $288 / 4 = 72$ boxes.
3.2.3 Calculate the cost of the tiles The cost of the tiles is the number of boxes times the cost per box: $72 \times R143.84 = R10356.48$
3.2.3 Calculate the number of cement bags needed The number of cement bags needed is the total area divided by the coverage per bag: $32 \text{ m}^2 / 3 \text{ m}^2 \approx 10.67 $ bags. Round up to 11 bags.
3.2.3 Calculate the cost of the cement The cost of cement is the number of bags times the cost per bag: $11 \times R99.90 = R1098.90$.
3.2.3 Calculate the cost of the grout The cost of the grout is $4 \times R89.90 = R359.60$.
3.2.3 Calculate the total cost of the project The total project cost is the sum of the tile cost, cement cost, grout cost, and labor cost: $R10356.48 + R1098.90 + R359.60 + R2500 = R14314.98$.
3.2.3 Determine if the budget is sufficient Since $R14314.98 < R15000$, Tshego's budget is enough.
3.2.1: $20 \text{ m}^2 + 12 \text{ m}^2 = 32 \text{ m}^2$ 3.2.2: 72 boxes 3.2.3: The total cost is $R14314.98$, which is less than the budget of $R15000$, so the budget is sufficient.
More Information
The solution requires careful unit conversion (cm to m), correct area calculation using the formula provided, and rounding up in several instances (number of tiles, bags of cement) since you can't buy fractions of these items.
Tips
- Forgetting to convert the tile size from cm to m before calculating the area.
- Not adding the extra 10% of tiles for wastage.
- Forgetting to round up to the nearest whole number when calculating the number of tile boxes or cement bags needed.
- Making arithmetic errors in the cost calculations.
- Not including all costs in the final budget calculation
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