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Let's solve the given problem step by step.

### Part (a)
We are asked to write an expression for the father's present age in terms of the son's age, \( s \).

- Let \( s \) represent the son's present age.
- The father is 32 years older than the son.

Thus, the father's present age can be expressed as:
\[
\text{Father's age} = s + 32
\]

### Part (b)
We are asked to form an equation based on the information that **10 years ago, the father was three times as old as his son**.

- 10 years ago, the son's age was \( s - 10 \).
- 10 years ago, the father's age was \( (s + 32) - 10 = s + 22 \).

According to the problem, 10 years ago, the father was three times as old as his son:
\[
s + 22 = 3(s - 10)
\]

Now, solve this equation:
\[
s + 22 = 3(s - 10)
\]
Distribute the 3 on the right side:
\[
s + 22 = 3s - 30
\]
Move all terms involving \( s \) to one side and constants to the other:
\[
22 + 30 = 3s - s
\]
Simplify:
\[
52 = 2s
\]
Solve for \( s \):
\[
s = \frac{52}{2} = 26
\]

So, the son is **26 years old**. Now, to find the father's present age:
\[
\text{Father's age} = s + 32 = 26 + 32 = 58
\]

Thus, the father is **58 years old**.

---

Would you like further details or clarification? 

Here are five related questions:
1. How would the equation change if the age difference between father and son were 25 years instead of 32?
2. What if 5 years ago, the father was twice as old as the son—how would you adjust the equation?
3. Can you generalize an equation to relate father and son’s ages based on different time gaps?
4. What would the father's age be if the son were currently 30 years old?
5. If the son's current age is unknown, how can we express both ages algebraically?

**Tip**: When setting up word problems, always define variables clearly and translate each part of the statement into equations step by step.

A man is 32 years older than his son. Ten years ago he was three times as old as his son was then.
a. If s represents the son’s present age, write an expression for the father’s present age in terms of s.
b. Form an equation in s using the above information and solve it to find the father’s present age.

Learn how to solve a word problem involving the age difference between a man and his son. This solution covers forming equations and solving for unknowns using algebraic expressions. Ideal for students in Grades 8-10.

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