Jane bought a new car three years ago. At the end of the first year the value of the car had decreased by 12.5%. The value of the car then decreased by 10% each year for the next two years. At the end of the three years, the value of the car was £17100. Work out the value of the car when Jane bought it three years ago.

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Jane bought a new car three years ago - Edexcel - GCSE Maths - Question 10 - 2022 - Paper 3

Question 10

Jane bought a new car three years ago. At the end of the first year the value of the car had decreased by 12.5%. The value of the car then decreased by 10% each yea... show full transcript

Worked Solution & Example Answer:Jane bought a new car three years ago - Edexcel - GCSE Maths - Question 10 - 2022 - Paper 3

Step 1

At the end of the first year, the value of the car decreased by 12.5%

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Answer

Let the original value of the car be represented as V. After the first year, the value can be expressed as:

$V \times (1 - 0.125) = V \times 0.875$

Step 2

At the end of the second year, the value decreased by 10%

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Answer

After the second year, the value will be:

$V \times 0.875 \times (1 - 0.10) = V \times 0.875 \times 0.90 = V \times 0.7875$

Step 3

At the end of the third year, the value decreased by 10% again

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Answer

After the third year, the value will be:

$V \times 0.7875 \times (1 - 0.10) = V \times 0.7875 \times 0.90 = V \times 0.70875$

Step 4

Setting the equation to find the original value

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Answer

According to the problem, at the end of three years, the value of the car was £17100. Thus, we can write:

$V \times 0.70875 = 17100$

To find V, we rearrange the equation:

$V = \frac{17100}{0.70875}$

Calculating this gives:

$V \approx 24100$

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