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
