A company offers two salary schemes for a 10-year period, Year 1 to Year 10 inclusive - Edexcel - A-Level Maths Pure - Question 1 - 2012 - Paper 1

Using the equivalence of total salary between the two schemes:

• The total earned under Scheme 2 can also be calculated with T:

  S_{10} = rac{10}{2} [2(P + 1800) + 9T]

  Setting them equal gives:

  $10P + 907 = 5 [2(P + 1800) + 9T]$

  This results in:

  $10P + 907 = 10P + 18000 + 45T$

  Rearranging gives:

  $45T = 907 - 18000 = -17093$

  Therefore:

  T = rac{-17093}{45} = -379.84.

  The positive value for T differs from typical salary increments, indicating further examination or bounds on salary increments might be required.

Given the value of T, we know Income in Year 10 for Scheme 2 is £29,850. Therefore, we can write the equation:

• For Year 10:

  $P + 1800 + 9T = 29850.$

  Substitute T to solve for P:

  $P + 1800 + 9 imes (-379.84) = 29850.$
  Simplifying this gives:

  $P + 1800 - 3418.56 = 29850,$

  which leads to:

  $P = 29850 + 3418.56 - 1800 = 24450.$

  Thus, the value of P is £24,450.