The sum of the present ages of five children who were born at intervals of 3 years each is 50 years. What is the present age of the youngest child in years?

Introduction / Context:
This problem involves ages of several children born at equal time intervals. It tests understanding of arithmetic progressions and how to model such situations using simple algebra. The key is to represent the ages in terms of the youngest child and then use the given total to solve for that youngest age.

Given Data / Assumptions:

• There are 5 children.
• They were born at intervals of 3 years each.
• The sum of their present ages is 50 years.
• We are asked to find the present age of the youngest child.
• All ages are assumed to be non-negative and measured in years.

Concept / Approach:
The ages of the children form an arithmetic progression because the difference between consecutive ages is constant, equal to 3 years. If the youngest child has age x years, the others will have ages x + 3, x + 6, x + 9 and x + 12 years. The sum of these five expressions must equal the total given in the problem. We can then solve the resulting linear equation for x.

Step-by-Step Solution:
Let the age of the youngest child be x years.Then the ages of the other four children are x + 3, x + 6, x + 9 and x + 12 years.Write the equation for the sum of the ages: x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50.Combine like terms: 5 * x + (3 + 6 + 9 + 12) = 50.Compute the constant sum: 3 + 6 + 9 + 12 = 30.So we have: 5 * x + 30 = 50.Subtract 30 from both sides: 5 * x = 20.Divide by 5: x = 20 / 5 = 4 years.

Verification / Alternative check:
Youngest child: 4 years.Other children: 7 years, 10 years, 13 years and 16 years.Check the total: 4 + 7 + 10 + 13 + 16 = 50 years, which matches the given sum.Therefore the age of the youngest child is correctly found as 4 years.

Why Other Options Are Wrong:
8 years: If the youngest age is 8, the ages would be 8, 11, 14, 17 and 20, whose sum is 70, not 50.10 years: If the youngest is 10, the sequence becomes 10, 13, 16, 19 and 22, summing to 80, not 50.None of these: This is incorrect because we have found a valid option, 4 years, that satisfies all conditions.

Common Pitfalls:
Some learners mistakenly take the oldest child as x and then add intervals backward, which complicates the algebra.Others may forget to multiply x by 5 when combining like terms, leading to an incorrect equation.A few students attempt guess-and-check, which can work here, but it is less systematic than forming an equation.

Final Answer:
The present age of the youngest child is 4 years.