Four years ago a man was 6 times as old as his son. after 16 years he will be twice as old as his son. what is the present age of man and his son?

General
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four years ago a man was 6 times as old as his son. after 16 years he will be twice as old as his son. what is the present age of man and his son?

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LectureNotes said four years ago a man was 6 times as old as his son. After 16 years he will be twice as old as his son. What is the present age of the man and his son?

Answer:
To solve this problem, let’s use algebra to set up equations based on the information given.

  1. Define the Variables:

    • Let ( m ) be the present age of the man.
    • Let ( s ) be the present age of the son.

  2. Set Up the Equations:

    • Four years ago, the man was 6 times as old as his son.
      • This translates to: ( m - 4 = 6(s - 4) )
    • Sixteen years from now, the man will be twice as old as his son.
      • This translates to: ( m + 16 = 2(s + 16) )

  3. Solve the Equations:

    First Equation:
    m - 4 = 6(s - 4)
    Simplify this equation:
    m - 4 = 6s - 24
    Rearrange to isolate ( m ):
    m = 6s - 20

    Second Equation:
    m + 16 = 2(s + 16)
    Simplify this equation:
    m + 16 = 2s + 32
    Rearrange to isolate ( m ):
    m = 2s + 16

  4. Equate the Two Expressions for ( m ):
    6s - 20 = 2s + 16
    Solve for ( s ):
    6s - 2s = 16 + 20
    4s = 36
    s = 9

    Now, substitute ( s ) back into one of the equations to find ( m ):
    m = 2s + 16
    m = 2(9) + 16
    m = 18 + 16
    m = 34

Conclusion:

  • The present age of the man (( m )) is ( 34 ) years.
  • The present age of the son (( s )) is ( 9 ) years.

Therefore, the man is 34 years old, and his son is 9 years old.