Find the number x such that, when x is added to itself 13 times (that is, 14x altogether), the result is 112. What is x?

Introduction / Context:
This arithmetic problem examines precise interpretation of phrasing and linear equations. “Added to itself 13 times” means the original number plus 13 more copies of the same number, yielding 14 copies in total. We then solve for the unknown x.

Given Data / Assumptions:

• The phrase implies total copies = 14.
• Total sum of these copies = 112.

Concept / Approach:
Translate the statement into a simple algebraic equation. If a number x is added to itself 13 times, there are 14x altogether. Set 14x = 112 and solve using basic division.

Step-by-Step Solution:
Let x be the number.“Added to itself 13 times” → total copies = 1 + 13 = 14, so sum = 14 * x.Given: 14 * x = 112.Divide both sides by 14: x = 112 / 14 = 8.

Verification / Alternative check:
Compute 14 * 8 = 112. The equality holds, confirming x = 8.

Why Other Options Are Wrong:

• 7, 9, 11, 6: 14 times any of these does not produce 112 (98, 126, 154, 84 respectively).

Common Pitfalls:

• Misreading “added to itself 13 times” as 13x instead of 14x, which would yield a non-integer not among options.

Final Answer:
8