Question

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.

Answer 1

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