Solve the problem using polya's steps            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 thier current ages.

To solve this problem using Polya's four-step problem-solving process, we’ll break it down step by step:

### Step 1: **Understand the Problem**
We are given two key pieces of information:
1. The sum of the ages of a father and his son is 45 years.
2. In 5 years, the father will be twice as old as his son.

We need to determine their current ages.

### Step 2: **Devise a Plan**
Let’s define the unknowns as:
- \( f \) = the father's current age
- \( s \) = the son's current age

From the given information, we can create two equations:
1. The sum of their ages is 45:  
   \[
   f + s = 45
   \]
2. In 5 years, the father will be twice as old as the son:  
   \[
   f + 5 = 2(s + 5)
   \]

Now, we have two equations, and we can solve them using substitution or elimination.

### Step 3: **Carry Out the Plan**
We’ll use substitution to solve this system of equations.

From the first equation, solve for \( f \):
\[
f = 45 - s
\]

Substitute \( f = 45 - s \) into the second equation:
\[
(45 - s) + 5 = 2(s + 5)
\]
Simplify and solve for \( s \):
\[
50 - s = 2(s + 5)
\]
\[
50 - s = 2s + 10
\]
Move all terms involving \( s \) to one side:
\[
50 - 10 = 2s + s
\]
\[
40 = 3s
\]
\[
s = \frac{40}{3} = 13.33
\]

Now that we know \( s \), the son’s age is approximately 13.33 years.

To find the father's age, substitute \( s \) back into \( f + s = 45 \):
\[
f + 13.33 = 45
\]
\[
f = 45 - 13.33 = 31.67
\]

Thus, the father's age is approximately 31.67 years.

### Step 4: **Look Back**
Let’s check if these ages make sense:
- The sum of their ages is \( 31.67 + 13.33 = 45 \), which matches the given information.
- In 5 years, the father will be \( 31.67 + 5 = 36.67 \), and the son will be \( 13.33 + 5 = 18.33 \). 
- The father’s age in 5 years is approximately double the son’s age, since \( 36.67 \approx 2 \times 18.33 \).

Therefore, the solution seems correct.

### Conclusion:
- The father's age is approximately 31.67 years.
- The son's age is approximately 13.33 years.

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Here are 5 related questions to further practice:

1. If the sum of a mother and daughter's age is 50, and in 10 years the mother will be three times as old as the daughter, what are their current ages?
2. A father is three times as old as his son now. In 10 years, the sum of their ages will be 80. How old are they now?
3. The sum of the ages of two sisters is 30. In 5 years, the older sister will be twice the younger one’s age. What are their current ages?
4. A man is twice as old as his niece. The sum of their ages is 36. How old are they both?
5. The sum of a grandfather and grandson’s age is 68. In 10 years, the grandfather will be four times as old as the grandson. What are their current ages?

### Tip:
When dealing with word problems involving ages, translating the information into mathematical equations is the key to simplifying the process. Always define variables carefully!

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.

Solve a word problem where the sum of a father and son's ages is 45, and in 5 years, the father will be twice as old as the son. This solution uses algebraic equations and is suitable for students in Grades 6-8.

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