Aftab tells his daughter, seven years …

Assume the present age of Aftab be x years and his daughter be y years. Present age of Aftab = x years and his daughter = y years Therefore, 7 years ago, age of Aftab = (x - 7) years and his daughter = (y - 7) years Using this information and applying the known condition that 7 years ago, Aftab was 7 times as old as his daughter then: x - 7 = 7(y - 7) x - 7 = 7y - 49 x - 7y - 7 + 49 = 0 x - 7y + 42 = 0 After 3 years from now, age of Aftab = (x + 3) years and his daughter's age = (y + 3) years Also, Aftab will be 3 times as old as his daughter which can be represented as: x + 3 = 3 (y + 3) x + 3 = 3y + 9 x - 3y + 3 - 9 = 0 x - 3y - 6 = 0 Thus we have, x - 7y + 42 = 0 ----(1) x - 3y - 6 = 0 ----(2) Therefore, the algebraic representation is for equation (1) is: x - 7y + 42 = 0 -7y = - x - 42 7y = x + 42 y = (x + 42)/7 And, algebraic representation for equation (2) is: x - 3y - 6 = 0 - 3y = - x + 6 3y = x - 6 y = (x - 6)/3 Let us represent these equations graphically. For this, we need at least two solutions for each equation. Let's tabulate the solutions. For equation (1), x = 21 y = (x + 42)/7 = 9 For equation (2), x =30 y = (x - 6)/3= 8. By doing graphical representation we got The present age of aftab 52 years and his daughter is 12 years old