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 14 - 2022 - Paper 3

Question 14

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 14 - 2022 - Paper 3

Step 1

At the end of the first year, what was the value?

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Answer

Let the initial value of the car be represented as $x$ . After the first year, the value decreases by 12.5%, thus the remaining value is:

$x imes (1 - 0.125) = x imes 0.875$

Step 2

At the end of the second year, what was the value?

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Answer

For the second year, the value will decrease by 10%. The value at the end of the second year is:

$0.875x imes (1 - 0.10) = 0.875x imes 0.90 = 0.7875x$

Step 3

At the end of the third year, what was the value?

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Answer

For the third year, again the value decreases by 10%. Thus, the value at the end of the third year is:

$0.7875x imes (1 - 0.10) = 0.7875x imes 0.90 = 0.70875x$

Setting this equal to the final value gives:

$0.70875x = 17100$

To find the value of the car when Jane bought it:

$x = \frac{17100}{0.70875} \\ x \approx 24100$

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