Your mother is 25 years older than you. Your father is 3 years older than your mother. The product of all three ages are 32,130. How old is your father?
Let my age ==A
Mother's age ==25 + A
Father's age ==25 + 3 + A
A * [25 + A] * [28 + A] ==32130, solve for A
Solve for A:
A (A + 25) (A + 28) = 32130
Expand out terms of the left hand side:
A^3 + 53 A^2 + 700 A = 32130
Subtract 32130 from both sides:
A^3 + 53 A^2 + 700 A - 32130 = 0
The left hand side factors into a product with two terms:
(A - 17) (A^2 + 70 A + 1890) = 0
Split into two equations:
A - 17 = 0 or A^2 + 70 A + 1890 = 0
Add 17 to both sides:
A = 17 or A^2 + 70 A + 1890 = 0
Subtract 1890 from both sides:
A = 17 or A^2 + 70 A = -1890
Add 1225 to both sides:
A = 17 or A^2 + 70 A + 1225 = -665
Write the left hand side as a square:
A = 17 or (A + 35)^2 = -665
Take the square root of both sides:
A = 17 or A + 35 = i sqrt(665) or A + 35 = -i sqrt(665)
Subtract 35 from both sides:
A = 17 or A = i sqrt(665) - 35 or A + 35 = -i sqrt(665)
Subtract 35 from both sides:
A = 17 years - my age
17 + 25 ==42 years- Mother's age
42 + 3==45 years - Father's age
Check: [17 x 42 x 45] ==32,130
