Linear equation from a percent-like fraction of a number: When 20 is subtracted from a number, the result equals seven-twelfths of that number. What is the sum of the digits of the number?

Introduction / Context:
This algebra problem expresses a number reduced by 20 as a fixed fraction of itself. Solving the resulting linear equation gives the number, and then its digit sum is requested.

Given Data / Assumptions:

• N − 20 = (7/12) * N
• N is a whole number (implied by digit-sum question)

Concept / Approach:
Bring all N terms to one side and constants to the other. Solve for N and compute its digit sum.

Step-by-Step Solution:
N − (7/12)N = 20(5/12)N = 20 → N = 20 * (12/5) = 48Sum of digits of 48 = 4 + 8 = 12

Verification / Alternative check:
Check: 48 − 20 = 28 and (7/12)*48 = 28, consistent.

Why Other Options Are Wrong:
44 and 48 are the number itself or irrelevant; 16 and 10 are incorrect digit sums for N = 48.

Common Pitfalls:
Sign errors or misinterpreting “seven-twelfths of the number” as something like N − 7/12 rather than (7/12) * N.

Final Answer:
12