Linear equation from a verbal sentence: If 24 is subtracted from a number, the result is four-sevenths of the original number. What is the sum of the digits of that number?

Introduction / Context:
Translate the statement into an equation, solve for the number, then compute the sum of its digits. This is a straightforward linear equation in one variable with a follow-up digit-sum calculation.

Given Data / Assumptions:

• x − 24 = (4/7) x.
• x is an integer (implied by a sensible “digits” question).

Concept / Approach:
Collect x terms on one side. Solve for x by isolating it using standard algebra. Then add the digits of the resulting number.

Step-by-Step Solution:

Verification / Alternative check:
Check the sentence: 56 − 24 = 32 and (4/7)*56 = 32. Equality holds; digit sum 11 is confirmed.

Why Other Options Are Wrong:

• 1, 9: Not the digit sum of 56.
• Data inadequate: The equation uniquely determines x.

Common Pitfalls:
Subtracting in the wrong direction or mishandling fractions when moving terms. Multiply both sides as needed to avoid fraction errors.

Final Answer: