Here is the floor plan of a rectangular room. 4.5 m 3 m Tim buys carpet tiles for this room. Each tile is a square measuring 50 cm by 50 cm. The tiles are only sold in packs of ten. Each pack costs £20. Tim pays for fitting at a rate of £7.50 per square metre, with any fraction of a square metre rounded up. Work out the total cost of the tiles and fitting.

GCSE OCR Maths Area: Here is the floor plan of a rect

Here is the floor plan of a rectangular room - OCR - GCSE Maths - Question 7 - 2018 - Paper 1

Question 7

Here is the floor plan of a rectangular room. 4.5 m 3 m Tim buys carpet tiles for this room. Each tile is a square measuring 50 cm by 50 cm. The tiles are only so... show full transcript

Worked Solution & Example Answer:Here is the floor plan of a rectangular room - OCR - GCSE Maths - Question 7 - 2018 - Paper 1

Step 1

Calculate the area of the room

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Answer

The area of the rectangular room can be calculated using the formula:

ext{Area} = ext{length} imes ext{width}

Substituting the given dimensions:

ext{Area} = 4.5 ext{ m} imes 3 ext{ m} = 13.5 ext{ m}^2

Step 2

Determine the number of tiles needed

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Answer

Each tile has an area of:

ext{Area of one tile} = 0.5 ext{ m} imes 0.5 ext{ m} = 0.25 ext{ m}^2

To find the total number of tiles required, divide the total area of the room by the area of one tile:

ext{Number of tiles} = rac{13.5 ext{ m}^2}{0.25 ext{ m}^2} = 54 ext{ tiles}

Step 3

Calculate the number of packs needed

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Answer

Since tiles are sold in packs of ten, the number of packs required is:

ext{Number of packs} = rac{54}{10} = 5.4 ext{ packs}

Rounding up, Tim needs to buy 6 packs of tiles.

Step 4

Calculate the cost of the tiles

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Answer

Given that each pack costs £20, the total cost for the tiles is:

ext{Cost of tiles} = 6 ext{ packs} imes £20 = £120

Step 5

Calculate the fitting cost

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Answer

Tim pays for fitting based on the area of the room:

ext{Fitting cost} = 13.5 ext{ m}^2 imes £7.50 ext{ per m}^2 = £101.25

Since we round up any fraction of a square metre, the cost becomes:

ext{Fitting cost (rounded up)} = £105

Step 6

Determine the total cost

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Answer

Finally, the total cost of the tiles and fitting is:

ext{Total cost} = ext{Cost of tiles} + ext{Fitting cost} = £120 + £105 = £225

Here is the floor plan of a rectangular room - OCR - GCSE Maths - Question 7 - 2018 - Paper 1

Worked Solution & Example Answer:Here is the floor plan of a rectangular room - OCR - GCSE Maths - Question 7 - 2018 - Paper 1

Calculate the area of the room

Determine the number of tiles needed

Calculate the number of packs needed

Calculate the cost of the tiles

Calculate the fitting cost

Determine the total cost

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