Four children spaced by 4 years: The average age is 12 years. If consecutive age gaps are 4 years, what is the age of the youngest child?

Introduction / Context:
An arithmetic progression model fits siblings with equal spacing. Represent ages in terms of the youngest and sum to match the given average.

Given Data / Assumptions:

• Four children; average = 12 ⇒ total = 48.
• Spacing between consecutive ages = 4 years.

Concept / Approach:
Let youngest = a. Then ages are a, a + 4, a + 8, a + 12. Sum equals 4a + 24; set equal to 48 and solve for a.

Step-by-Step Solution:

Verification / Alternative check:
Ages become 6, 10, 14, 18 with sum 48; average is 12, consistent with the prompt.

Why Other Options Are Wrong:

• 7, 8, 9 years: Do not satisfy the sum required by the given average and spacing.

Common Pitfalls:
Using the average as the youngest directly or ignoring that four terms are spread symmetrically around the mean.

Final Answer: