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Today I am 6 years less than half my father's age 6 years, I will be 6 years more than one-third my father's age. How old was my father when I was born?

Today I am 66 years less than half my father's age 66 years, I will be 66 years more than one-third my father's age. How old was my father when I was born?

Full solution

Q. Today I am 66 years less than half my father's age 66 years, I will be 66 years more than one-third my father's age. How old was my father when I was born?
  1. Define Variables: Let xx be my current age and yy be my father's current age.\newlineThe first condition says I am 66 years less than half my father's age: x=(12)y6x = (\frac{1}{2})y - 6.
  2. Set Up Equations: The second condition says in 66 years, I will be 66 years more than one-third my father's age: x+6=(13)(y+6)+6x + 6 = (\frac{1}{3})(y + 6) + 6.
  3. Solve for x: Now we have two equations:\newline11) x=12y6x = \frac{1}{2}y - 6\newline22) x+6=13(y+6)+6x + 6 = \frac{1}{3}(y + 6) + 6\newlineLet's solve the second equation for x: x=13y+2+66x = \frac{1}{3}y + 2 + 6 - 6.

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