Question

A varies directly as the sum of the quantities BC. Biturn varies directly as x and C varies inversely as x. When x =2, A =6 and when x =4,A =9. Find the value of A when the value of x=16.

Answer 1

A α B + C  → A = k (B + C)
Also, B α x  so  B = k₁x  and  C α 1/x   so C = k₂/x
Therefore A = kk₁x + kk₂/x  =  p₁x + p₂/x  (where p₁ and p₂ are constants)
→ 2p₁ + p₂/2 = 6
→ 4p₁ + p₂ = 12          → 1
And 4p₁ + p₂/4 = 9
→ 16p₁ + p₂ = 36         → 2
Solving (1) and (2), we get   p₁ = 2  and  p₂ = 4
Therefore  A = 2x + 4/x
When x = 16,  A = 32 + ¼ = 32¼