https://file.aiquickdraw.com/mathbot/file/1728372299342ojs9rk4z.jpg

Let's break down the problem step by step:

Let the present age of the son be \( x \) years.

According to the first condition:
- The present age of the father is four times the age of the son, so the father's current age is \( 4x \) years.

Now, for the second condition:
- In 10 years, the father's age will be \( 4x + 10 \), and the son's age will be \( x + 10 \).
- At that time, the father's age will be three times the son's age, so we have the equation:
\[
4x + 10 = 3(x + 10)
\]

### Solve for \( x \):
\[
4x + 10 = 3(x + 10)
\]
Expand the right side:
\[
4x + 10 = 3x + 30
\]
Now, subtract \( 3x \) from both sides:
\[
x + 10 = 30
\]
Subtract 10 from both sides:
\[
x = 20
\]

### Conclusion:
The son is 20 years old. Since the father's age is four times the son's age:
\[
\text{Father's age} = 4 \times 20 = 80
\]

Thus, the present ages are:
- The son is 20 years old.
- The father is 80 years old.

Would you like more details or have any questions?

Here are some related questions to consider:
1. How would the equation change if the father were five times the son’s age instead of four?
2. What if the time period were 15 years instead of 10 years?
3. How does the solution change if the son's current age is unknown but given as a proportion?
4. How can we set up the problem if the father’s age is known, but the son's age is to be found?
5. How would the equation adjust if we introduce a different relationship, such as a fractional or non-integer ratio of their ages?

**Tip**: When solving word problems, always define variables clearly and translate conditions directly into mathematical expressions.

The present age of father is four times the age of his son. After ten years, age of his father will become three times the age of his son. Find their present ages.

Solve the problem where a father's current age is four times his son's, and after 10 years, the father's age will be three times the son's age. Learn how to set up linear equations and solve for present ages using algebra.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation