Here is the floor plan of a rectangular room. 4.5 m 3 m Not to scale Tim buys carpet tiles for this room. Each tile is a square measuring 50cm by 50cm. 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 15 - 2018 - Paper 1

Question 15

Here is the floor plan of a rectangular room. 4.5 m 3 m Not to scale Tim buys carpet tiles for this room. Each tile is a square measuring 50cm by 50cm. The tile... show full transcript

Worked Solution & Example Answer:Here is the floor plan of a rectangular room - OCR - GCSE Maths - Question 15 - 2018 - Paper 1

Step 1

Calculate the area of the room in square meters

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Answer

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

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

In this case:

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

Step 2

Calculate the number of tiles needed

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Answer

Each tile measures 0.5m x 0.5m, which is equivalent to:

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

To find the total number of tiles needed:

ext{Number of tiles} = rac{ ext{Area of the room}}{ ext{Area of one tile}} = rac{13.5}{0.25} = 54 ext{ tiles}

Step 3

Calculate the number of packs of tiles needed

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Answer

Since the tiles are sold in packs of ten, we need:

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

Rounding up, Tim needs 6 packs.

Step 4

Calculate the cost of the tiles

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Answer

The cost for one pack is £20, so:

ext{Cost of tiles} = 6 imes 20 = £120

Step 5

Calculate the fitting cost

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Answer

The fitting cost is based on the area of the room. The area is 13.5 m², which rounds up to 14 m²:

ext{Fitting cost} = 14 imes 7.5 = £105

Step 6

Calculate the total cost of tiles and fitting

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Answer

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

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 15 - 2018 - Paper 1

Worked Solution & Example Answer:Here is the floor plan of a rectangular room - OCR - GCSE Maths - Question 15 - 2018 - Paper 1

Calculate the area of the room in square meters

Calculate the number of tiles needed

Calculate the number of packs of tiles needed

Calculate the cost of the tiles

Calculate the fitting cost

Calculate the total cost of tiles and fitting

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