The sum of the ages of a father and son is 45 years. the father is four times as old as the son. What are their ages

Let the son's age be \( x \) years. Since the father is four times as old as the son, the father's age is \( 4x \) years. 

According to the problem, the sum of their ages is 45 years. This gives us the equation:

\[
x + 4x = 45
\]

Simplifying this:

\[
5x = 45
\]

Now, solve for \( x \):

\[
x = \frac{45}{5} = 9
\]

So, the son's age is 9 years. Since the father is four times the son's age, the father's age is:

\[
4 \times 9 = 36
\]

Thus, the son is 9 years old, and the father is 36 years old.

### Summary:
- Son's age: 9 years
- Father's age: 36 years

Would you like more details or have any questions?

### 5 Related Questions:
1. What would be their ages if the father was three times as old as the son?
2. How would the equation change if the sum of their ages was 50 instead of 45?
3. What if the father was only two times as old as the son, with the same sum of ages?
4. How can this problem be represented graphically on a coordinate plane?
5. How would the ages change if the father was five times as old as the son?

### Tip:
When solving word problems, it's helpful to assign variables and set up an equation based on the relationships described in the problem.

The sum of the ages of a father and son is 45 years. The father is four times as old as the son. What are their ages?

This problem involves finding the ages of a father and son, where the sum of their ages is 45 years and the father is four times as old as the son. Learn how to set up and solve linear equations step-by-step. This problem is suitable for students in Grades 6-8.

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