Problem 85 - College Algebra

Question

In a film, the actor Charles Coburn plays an elderly "uncle" character criticized for marrying a woman when he is 3 times her age. He wittily replies, "Ah, but in 20 years time I shall only be twice her age." How old is the "uncle" and the woman?

Step-by-Step Solution

Answer

The 'uncle' is currently 60 years old and the woman is 20 years old.

Step 1: Formulate the Equations

Let's denote the 'uncle's' current age as \( U \) and the woman's current age as \( W \). From the problem, we know that \( U = 3W \) (the 'uncle' is three times as old as the woman). We also know that in twenty years, the 'uncle' will be twice as old as the woman, expressed as \( U + 20 = 2 \)( \( W + 20 \) ). We now have a system of two equations that describe the given age conditions.

Step 2: Solve the System of Equations

To solve the system, one can substitute \( U \) from the first equation into the second equation. This gives us: \( 3W + 20 = 2 \)( \( W + 20) \). Expanding the brackets and simplifying the equation we get: \( 3W + 20 = 2W + 40 \). By subtracting \( 2W \) and 20 from both sides, we find that \( W = 20 \). Now we can substitute \( W = 20 \) into the first equation to solve for \( U \). Doing this we find that \( U = 3 \)( \( W \) ) = 3 \)( \( 20 \) ) = 60.

Step 3: Interpret the Results

The solution to our system of equations gives the 'uncle's' current age as 60 years and the woman's current age as 20 years.