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Let's define the ages of James and Arthur based on the given conditions:

- Let \( A \) represent Arthur's current age.
- James is currently 3 times as old as Arthur, so James' current age is \( 3A \).

In 10 years:
- Arthur's age will be \( A + 10 \).
- James' age will be \( 3A + 10 \).

According to the problem, in 10 years, James will be twice as old as Arthur. Thus, we can set up the following equation:

\[
3A + 10 = 2(A + 10)
\]

Now let's solve this equation:

\[
3A + 10 = 2A + 20
\]

Subtract \( 2A \) from both sides:

\[
A + 10 = 20
\]

Subtract 10 from both sides:

\[
A = 10
\]

So, Arthur is currently 10 years old. Since James is 3 times Arthur's age, James is:

\[
3A = 3 \times 10 = 30
\]

Thus, James is currently 30 years old.

### Conclusion:
- Arthur is 10 years old.
- James is 30 years old.

Would you like a more detailed explanation or have any questions?

Here are 5 related questions you might find interesting:
1. What if James were 4 times as old as Arthur instead of 3 times?
2. How would the equation change if the age difference were given instead of a ratio?
3. What if the time period in the future was 20 years instead of 10?
4. Can you find a formula to generalize the relationship between their ages for any time frame?
5. How does the result change if we reverse the roles of James and Arthur in the problem?

**Tip:** When solving age-related problems, creating clear definitions of the variables and setting up equations based on given relationships is key to organizing your solution.

James is now 3 times as old as Arthur. In 10 years, James will be twice as old as Arthur will be. Find their present ages.

Learn how to solve an age-related word problem where James is 3 times as old as Arthur, and in 10 years, he will be twice as old as Arthur. This detailed explanation covers the use of linear equations to find their present ages. Suitable for students in Grades 7-8.

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