Sequential Transformations on a Number A number, when decreased by 4 and then divided by 6, gives 9. What is the result if instead the number is decreased by 3 and then divided by 5?

Introduction / Context:
Translate stepwise verbal operations into algebraic equations. First, recover the original number from the given condition. Then apply the new transformation and compute the final value exactly.

Given Data / Assumptions:

• (N − 4)/6 = 9.
• We must then compute (N − 3)/5.
• N is real (and will turn out to be integer).

Concept / Approach:
Solve the first linear equation for N. Substitute that value into the second expression to obtain the requested result. Mixed-number options indicate that exact division may produce an integer or a fractional result, so compute carefully.

Step-by-Step Solution:
(N − 4)/6 = 9 → N − 4 = 54 → N = 58.Compute (N − 3)/5 = (58 − 3)/5 = 55/5 = 11.

Verification / Alternative check:
Plug back: (58 − 4)/6 = 54/6 = 9, matching the initial condition. The second calculation is straightforward division yielding an integer.

Why Other Options Are Wrong:
9 2/5, 10 1/5, 11 2/5, and 10 4/5 correspond to incorrect substitutions or arithmetic slips. Only 11 matches the correct evaluation.

Common Pitfalls:
Subtracting 3 from 9 instead of from N; mixing order of operations; performing 55/5 incorrectly as a mixed number.

Final Answer:
11