Problem 87 - College Algebra Essentials

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 woman is 20 years old and the man is 60 years old

Step 1: Set up the equations

From the problem, we can set up two equations: \'At the time of their marriage': \(M = 3W\) and '20 years in the future': \(M + 20 = 2(W + 20)\)

Step 2: Substitute \(3W\) for \(M\) in the second equation

We can replace \(M\) with \(3W\) in the second equation to solve for \(W\). So, substituting we have: \(3W + 20 = 2(W + 20)\)

Step 3: Solve the equation

Solving the equation will give us the woman’s age:\First simplify the equation: \(3W + 20 = 2W + 40\) \Subtract \(2W\) from both sides: \(W = 20\)

Step 4: Find the man's age

Substitute \(W = 20\) into the first equation to find the man's age:\\(M = 3 * 20 = 60\)