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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.

User John Pang
by
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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
User Dilshan
by
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