Aaliyah bought a car - Edexcel - GCSE Maths - Question 10 - 2022 - Paper 2

To find the value of the car when Aaliyah bought it, we need to reverse the depreciation that occurred over the two years.

Step 1: Find the value of the car at the end of the first year.

Since the car depreciated by 19% in the second year, its value at the end of the first year (denote this value as V1) can be found using:

$V2 = V1 imes (1 - 0.19)$

Substituting the end value V2 = £10914.75:

$10914.75 = V1 imes 0.81$

Now, solve for V1:

$V1 = \frac{10914.75}{0.81} \approx 13421.60$

Step 2: Find the original value of the car when Aaliyah bought it.

Now, we know the value of the car at the end of the first year was approximately £13421.60. Since it depreciated by 23% in the first year, we can find the original value (denote this value as V0) as follows:

$V1 = V0 imes (1 - 0.23)$

Substituting the value of V1:

$13421.60 = V0 imes 0.77$

Now, solve for V0:

$V0 = \frac{13421.60}{0.77} \approx 17445.26$

Conclusion:

Thus, the value of the car when Aaliyah bought it was approximately £17445.26.