To determine the age of the youngest child, let's solve the problem step by step.

Problem Breakdown:

The ages of 4 children are given as being at intervals of 3 years each.
Let the age of the youngest child be $x$ years.

Thus, the ages of the children are:

1. $x$ (youngest),
2. $x + 3$,
3. $x + 6$,
4. $x + 9$.

The sum of their ages is given as $36$ years.

Formulating the Equation:

$x + (x + 3) + (x + 6) + (x + 9) = 36$

Simplify the equation:
$x + x + 3 + x + 6 + x + 9 = 36$ Combine like terms:
$4x + 18 = 36$

Solving for $x$:

Subtract 18 from both sides:
$4x = 18$

Divide by 4:
$x = \frac{18}{4} = 4.5$

Final Answer:

The age of the youngest child is 4.5 years.

Verify the Solution:

If $x = 4.5$, the ages are:

• $4.5$ (youngest),
• $7.5$ (next),
• $10.5$,
• $13.5$.

Add the ages:
$4.5 + 7.5 + 10.5 + 13.5 = 36$

This confirms the solution.

Answer: 4.5 years

Do you need further clarification or a detailed explanation of any step?

Related Questions:

1. What is the sum of ages if the children were born at intervals of 2 years instead?
2. How would the equation change if the sum of ages were 48 years?
3. What if the intervals were not equal but random? How would you set up the equation?
4. How do we solve similar problems using algebraic techniques?
5. What happens if the number of children increases while keeping the total sum constant?

Tip: Always simplify and combine like terms in an equation before solving for the variable.