A is a function of P . It is known that A is the sum of two parts, one part varies as P and the other part varies as the square of P . When P = 24 , A = 36 and when P = 18 , A = 9. Express A in terms of P .

Let A = aP + bP2 , where a and b are constants.
Sub. P = 24 , A = 36 ,
24a + 576b = 36
2a + 48b = 3 ………… (1)
Sub. P = 18 , A = 9 ,
18a + 324b = 9
2a + 36b = 1 ………… (2)
Solving (1) and (2)
a=-5/2

b=1/6

∴A=-5/2P + 1/6P2(square)