Raya buys a van for £8500 plus VAT at 20% Raya pays a deposit for the van. She then pays the rest of the cost in 12 equal payments of £531.25 each month. Find the ratio of the deposit Raya pays to the total of the 12 equal payments. Give your answer in its simplest form.

GCSE Edexcel Maths Coordinate Geometry: Raya buys a van for £8500 plus V

Raya buys a van for £8500 plus VAT at 20% Raya pays a deposit for the van - Edexcel - GCSE Maths - Question 5 - 2018 - Paper 2

Question 5

Raya buys a van for £8500 plus VAT at 20% Raya pays a deposit for the van. She then pays the rest of the cost in 12 equal payments of £531.25 each month. Find the ... show full transcript

Worked Solution & Example Answer:Raya buys a van for £8500 plus VAT at 20% Raya pays a deposit for the van - Edexcel - GCSE Maths - Question 5 - 2018 - Paper 2

Step 1

Find the total cost of the van including VAT

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Answer

The cost of the van before VAT is £8500. The VAT is calculated as follows:

[ \text{VAT} = 8500 \times 0.20 = 1700 ]

Thus, the total cost of the van is:

[ \text{Total Cost} = 8500 + 1700 = 10200 ]

Step 2

Find the total amount paid through equal payments

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Answer

Raya pays £531.25 each month for 12 months. The total amount paid through these payments is:

[ \text{Total Payments} = 531.25 \times 12 = 6375 ]

Step 3

Determine the deposit paid by Raya

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Answer

To find the deposit, we can subtract the total payments from the overall cost of the van:

[ \text{Deposit} = 10200 - 6375 = 3825 ]

Step 4

Find the ratio of the deposit to the total equal payments

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Answer

The ratio of the deposit to the total of the 12 equal payments is given by:

[ \text{Ratio} = \frac{\text{Deposit}}{\text{Total Payments}} = \frac{3825}{6375} ]

To simplify this, we can divide both the numerator and the denominator by 6375:

[ \text{Simplified Ratio} = \frac{3825 \div 6375}{6375 \div 6375} = \frac{\frac{3825}{6375}}{1} = \frac{61}{102} \text{ or } \frac{1}{1.67} ]

Thus, the ratio of the deposit to the total of the payments in simplest form is ( \frac{61}{102} ).

Raya buys a van for £8500 plus VAT at 20% Raya pays a deposit for the van - Edexcel - GCSE Maths - Question 5 - 2018 - Paper 2

Worked Solution & Example Answer:Raya buys a van for £8500 plus VAT at 20% Raya pays a deposit for the van - Edexcel - GCSE Maths - Question 5 - 2018 - Paper 2

Find the total cost of the van including VAT

Find the total amount paid through equal payments

Determine the deposit paid by Raya

Find the ratio of the deposit to the total equal payments

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