the sum of the ages of a father and his son is 45. in 5 years, the father will be twice as old as his son. find their current ages.

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!

The sum of the ages of a father and his son is 45. In 5 years, the father will be twice as old as his son. Find their current ages.

Discover how to solve an algebra problem where the sum of a father's and son's ages is 45, and in 5 years, the father will be twice as old as his son. This step-by-step solution uses key algebraic concepts and linear equations. Ideal for Grades 6-8.

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