Adjusted ratio with translated terms: If a/3 = b/8, find the ratio (a + 3) : (b + 8) in simplest form.

Introduction / Context:
When two variables are proportional via a/3 = b/8, we can parametrize them and then evaluate expressions like (a + constant) : (b + constant). This technique shows up in many ratio translation problems.

Given Data / Assumptions:
a/3 = b/8 with positive values for a and b.

Concept / Approach:
From a/3 = b/8 = k, write a = 3k and b = 8k. Then substitute into (a + 3) : (b + 8) and simplify.

Step-by-Step Solution:
Let a = 3k and b = 8k. Compute a + 3 = 3k + 3 = 3(k + 1). Compute b + 8 = 8k + 8 = 8(k + 1). Therefore, (a + 3) : (b + 8) = 3(k + 1) : 8(k + 1) = 3 : 8.

Verification / Alternative check:
Choose k = 1 → a = 3, b = 8. Then (a + 3) : (b + 8) = 6 : 16 = 3 : 8, confirming the result.

Why Other Options Are Wrong:
8 : 3 inverts the order; 5 : 8 or 11 : 16 do not arise from consistent parametrization; 3 : 5 truncates scaling incorrectly.

Common Pitfalls:
Forgetting to add constants to the correct variable or cancelling incorrectly; always factor out the common (k + 1) before cancelling.

Final Answer:
3 : 8