Analyzing the Father and Son Age Word Problem

This problem requires us to determine a future time point when a specific age relationship between a father and his son holds true. We are given information about their ages 3 years ago and need to find how many years from the present the father will be twice the son's age.

Setting Up Variables for Current Ages

Let's define the current ages algebraically:

• Let $F$ represent the father's current age in years.
• Let $S$ represent the son's current age in years.

Formulating the Equation Based on Past Ages

The question states that 3 years ago, the father's age was 18 years more than twice his son's age. We can write the ages 3 years ago as:

• Father's age 3 years ago: $F - 3$
• Son's age 3 years ago: $S - 3$

Using the information provided, we can set up the first equation:

$F - 3 = 2 \times (S - 3) + 18$

Simplifying the Equation for Current Ages

Let's simplify the equation derived from the past scenario to find the relationship between their current ages:

$F - 3 = 2S - 6 + 18$

$F - 3 = 2S + 12$

$F = 2S + 12 + 3$

$F = 2S + 15$

This simplified equation shows that the father's current age is 15 years more than twice the son's current age.

Formulating the Equation for Future Ages

We need to find the number of years from now when the father's age will be twice the son's age. Let $x$ be the number of years from the present moment.

• Father's age after $x$ years: $F + x$
• Son's age after $x$ years: $S + x$

The condition for the future is:

$F + x = 2 \times (S + x)$

Step-by-Step Calculation to Find 'x'

Now, we substitute the expression for the father's current age ($F = 2S + 15$) into the future age equation:

1. Substitute $F$: $(2S + 15) + x = 2(S + x)$
2. Distribute the 2 on the right side: $2S + 15 + x = 2S + 2x$
3. Subtract $2S$ from both sides of the equation: $15 + x = 2x$
4. Isolate $x$ by subtracting $x$ from both sides: $15 = 2x - x$ $15 = x$

The value $x = 15$ represents the number of years from the present time.

Conclusion of the Age Calculation

Therefore, after 15 years from now, the father's age will be exactly twice his son's age. This age calculation problem demonstrates the application of basic algebra to solve real-world scenarios involving time and relationships.