The diagram shows a floor in the shape of a trapezium. John is going to paint the floor. Each 5 litre tin of paint costs £16.99 1 litre of paint covers an area of 2 m² John has £160 to spend on paint. Has John got enough money to buy all the paint he needs? You must show how you get your answer.

GCSE Edexcel Maths Coordinate Geometry: The diagram shows a floor in the

The diagram shows a floor in the shape of a trapezium - Edexcel - GCSE Maths - Question 6 - 2018 - Paper 2

Question 6

The diagram shows a floor in the shape of a trapezium. John is going to paint the floor. Each 5 litre tin of paint costs £16.99 1 litre of paint covers an area of ... show full transcript

Worked Solution & Example Answer:The diagram shows a floor in the shape of a trapezium - Edexcel - GCSE Maths - Question 6 - 2018 - Paper 2

Step 1

Calculate the area of the trapezium

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Answer

The area of a trapezium can be calculated using the formula:

ext{Area} = rac{1}{2} imes ( ext{Base}_1 + ext{Base}_2) imes ext{Height}

In this case, Base_1 is 10 m, Base_2 is 16 m, and the height is 7 m. Therefore:

ext{Area} = rac{1}{2} imes (10 + 16) imes 7 = rac{1}{2} imes 26 imes 7 = 91 ext{ m}^2

Step 2

Determine the total coverage of the paint

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Answer

Each litre of paint covers an area of 2 m². Therefore, 1 tin (5 litres) covers:

5 ext{ litres} imes 2 ext{ m}^2/ ext{litre} = 10 ext{ m}^2

Step 3

Calculate the total number of tins needed

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Answer

To find the number of tins of paint needed, divide the total area by the coverage of one tin:

ext{Number of tins} = rac{91 ext{ m}^2}{10 ext{ m}^2/ ext{tin}} = 9.1 ext{ tins}

Since John cannot buy a fraction of a tin, he needs to round up to 10 tins.

Step 4

Calculate the total cost for the paint

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Answer

The cost of one tin is £16.99, so the total cost for 10 tins is:

ext{Total cost} = 10 ext{ tins} imes £16.99 = £169.90

Step 5

Determine if John has enough money

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Answer

John has £160, which is not enough to cover the total cost of £169.90. Therefore, the answer is:

No, John does not have enough money to buy all the paint he needs.

The diagram shows a floor in the shape of a trapezium - Edexcel - GCSE Maths - Question 6 - 2018 - Paper 2

Worked Solution & Example Answer:The diagram shows a floor in the shape of a trapezium - Edexcel - GCSE Maths - Question 6 - 2018 - Paper 2

Calculate the area of the trapezium

Determine the total coverage of the paint

Calculate the total number of tins needed

Calculate the total cost for the paint

Determine if John has enough money

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