Let's use algebra to solve the problem.

Let:

• $f$ represent the father's current age.
• $s$ represent the son's current age.

We are given two pieces of information:

1. The sum of the father's and son's current ages is 45: $f + s = 45 \quad \text{(Equation 1)}$

2. In 5 years, the father will be twice as old as the son: $f + 5 = 2(s + 5) \quad \text{(Equation 2)}$

Step 1: Solve Equation 2 for $f$

Simplify Equation 2: $f + 5 = 2(s + 5)$ Expanding the right-hand side: $f + 5 = 2s + 10$ Now, subtract 5 from both sides: $f = 2s + 5 \quad \text{(Equation 3)}$

Step 2: Substitute Equation 3 into Equation 1

Now, substitute $f = 2s + 5$ into Equation 1: $(2s + 5) + s = 45$ Simplify: $3s + 5 = 45$ Subtract 5 from both sides: $3s = 40$ Now, divide by 3: $s = \frac{40}{3} \approx 13.33$

Step 3: Solve for $f$

Now, substitute $s = 13.33$ back into Equation 3: $f = 2(13.33) + 5 = 26.67 + 5 = 31.67$

Final Answer:

The son is approximately 13.33 years old, and the father is approximately 31.67 years old.

Would you like a more detailed explanation of any step, or further questions about this?

Here are 5 follow-up questions you might explore:

1. What would their ages be if the sum of their ages was 50 instead of 45?
2. How would the solution change if the father were 3 times as old as his son in 5 years?
3. What if the father had been 3 times the son’s age 5 years ago?
4. How do the ages change if the sum of their ages was 60 but with the same second condition?
5. How would you solve this problem using a graph?

Tip: When solving word problems, clearly defining variables and writing out the conditions as equations can make the solution much easier to find!