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

To find the original value of the car when Aaliyah bought it, we need to work backward from the final value of the car at the end of the second year.

1. Calculate the value of the car at the beginning of the second year:

   • The car depreciated by 19% in the second year. Therefore, if the end value after the second year is £10914.75, we can represent the value at the beginning of the second year as:

   y * (1 - 0.19) = 10914.75

   Here, y represents the value at the beginning of the second year.

   • Rearranging the equation gives:

   y = \frac{10914.75}{0.81} = 13450.93

2. Calculate the value of the car at the time of purchase:

• Next, the car’s value depreciated by 23% in the first year, thus the value when Aaliyah bought it can be found similarly:

z * (1 - 0.23) = 13450.93

• Rearranging gives:

z = \frac{13450.93}{0.77} = 17403.85

Thus, the value of the car when Aaliyah bought it was approximately £17403.85.