Mrs. Tiwari has two sons, one being exactly one year older than the other. Her age is equal to the sum of the squares of the ages of her sons. If 4 years hence her age becomes five times the age of the elder son then find the ages of her sons.
Let x = child number 1 y = son number 2 z = Mrs. Tiwari We have then: y = x + 1 z = x ^ 2 + y ^ 2 z + 4 = 5(y+4) We solve the system: Equation1 y = x + 1 Equations 1 and 2: z = x ^ 2 + (x + 1) ^ 2 z = x ^ 2 + x ^ 2 + 2x + 1 z = 2x ^ 2 + 2x + 1 Equation 2 and 3 z + 4 = 5(y+4) 2x ^ 2 + 2x + 1 + 4 = 5 (x + 1 + 4) 2x ^ 2 + 2x + 5 = 5x + 25 2x ^ 2 + 2x- 5x + 5 - 25= 0 2x ^ 2-3x -20= 0 x = 4 Substituting: y = x + 1 y = 4 + 1 y = 5 answer: the ages of her sons are x = 4 y = 5
