Proportional ages with known mean: The average age of three boys is 15 years and their ages are in the ratio 3 : 5 : 7. Find the age of the oldest boy.

Introduction / Context:
When ages are proportional and the average is given, scale the ratio so the sum matches the total from the average. The largest part of the ratio yields the oldest age directly after scaling.

Given Data / Assumptions:

• Average of 3 = 15 → total = 45
• Age ratio = 3 : 5 : 7

Concept / Approach:
Let the common factor be k. Then ages are 3k, 5k, 7k and 3k + 5k + 7k = 15k must equal 45. Solve for k, then multiply to get the oldest age (7k).

Step-by-Step Solution:

Verification / Alternative check:
Ages are 9, 15, 21 with average (9 + 15 + 21)/3 = 45/3 = 15, satisfying all conditions.

Why Other Options Are Wrong:

• 7, 14, 20, 24: do not match the scaled 7k value with k = 3.

Common Pitfalls:
Using the mean directly as one of the ages or adding ratio numbers incorrectly (sum must be 15 parts).

Final Answer:
21 yr