The image contains a word problem that needs to be solved. Here is a transcribed version of the problem:

Problem: A man is three times as old as his son. In 7 years, he will be twice as old as his son will be then. Find their present ages. Show your work.

Solution:

Let the son's current age be $x$ years. Then, the man's current age is $3x$ years (since he is three times as old as his son).

In 7 years:

• The son's age will be $x + 7$ years.
• The man's age will be $3x + 7$ years.

According to the problem, in 7 years, the man will be twice as old as the son: $3x + 7 = 2(x + 7)$

Now, let's solve the equation:

1. Expand and simplify: $3x + 7 = 2x + 14$

2. Subtract $2x$ from both sides: $x + 7 = 14$

3. Subtract 7 from both sides: $x = 7$

So, the son is currently 7 years old.

The man's age is: $3x = 3(7) = 21$

Thus, the man is currently 21 years old.

Answer: The son is 7 years old, and the man is 21 years old.

Would you like more details on this solution or have any other questions?

Here are five related questions to deepen your understanding:

1. What would be the man's age when his son is 20 years old?
2. How would the equation change if the man were four times as old as his son?
3. Can you form a similar problem but with different age ratios and solve it?
4. What would happen to the solution if we changed the 7 years to 10 years?
5. How can you verify the solution by substituting the ages back into the problem?

Tip: When solving age-related word problems, clearly defining variables and setting up equations based on the relationships described is crucial.