The sum of two numbers equals twice their difference. If one number is 10, what is the other number?

Introduction / Context:
Verbal equations involving sums and differences require careful interpretation. Here, the sum of two numbers equals twice their difference. One of the numbers is given as 10; we must determine the other number consistent with this relationship.

Given Data / Assumptions:

• Known number = 10; unknown number = t.
• Sum equals twice the (positive) difference, so 10 + t = 2 * |10 − t|.
• We consider cases depending on whether t ≥ 10 or t ≤ 10.

Concept / Approach:
The absolute value in the difference requires case analysis. Solve separately for t ≥ 10 (difference is t − 10) and for t ≤ 10 (difference is 10 − t), then check which solution matches the options and the original equation.

Step-by-Step Solution:

Verification / Alternative check:
For t = 30: sum = 40; difference = 20; twice the difference = 40; equality holds. For t = 10/3, equality also holds, but that choice is not provided in the same exact form among the options (spacing aside), and typical test intent favors the integer solution.

Why Other Options Are Wrong:
31/ 3 (10 1/3) does not satisfy the intended integer solution pattern; 1/3 and 41/ 4 are extraneous; 20 fails the relation.

Common Pitfalls:
Dropping the absolute value and missing case analysis; choosing a plausible but unlisted fractional value; arithmetic slips when moving terms.

Final Answer:
30