Father's Age Problem Solution

Let Lima's current age be L years and her father's current age be F years.

Setting Up the Equations

Based on the problem statement:

• "Lima's father is four times as old as Lima": This translates to the equation:

  $ F = 4L $

• "Four years ago, his father was six times as old as he was then":
  • Four years ago, Lima's age was $ L - 4 $.
  • Four years ago, the father's age was $ F - 4 $.
  This translates to the equation:

  $ F - 4 = 6(L - 4) $

Solving for Lima's Age

Substitute the first equation ($ F = 4L $) into the second equation:

$ 4L - 4 = 6(L - 4) $

Distribute the 6 on the right side:

$ 4L - 4 = 6L - 24 $

Rearrange the terms to solve for L:

$ 24 - 4 = 6L - 4L $

$ 20 = 2L $

Divide by 2:

$ L = \frac{20}{2} $

$ L = 10 $

So, Lima's current age is 10 years.

Calculating Father's Age

Use the first equation ($ F = 4L $) to find the father's current age:

$ F = 4 \times 10 $

$ F = 40 $

The father's present age is 40 years.

Verification

Check the conditions:

• Present: Father (40) is 4 times Lima (10). $ 40 = 4 \times 10 $. (True)
• 4 years ago: Father was $ 40 - 4 = 36 $. Lima was $ 10 - 4 = 6 $. Was the father 6 times Lima's age? $ 36 = 6 \times 6 $. (True)

Both conditions are satisfied.