Number System — A number is as much greater than 31 as it is less than 55. Determine the number (the value exactly halfway between 31 and 55).

Introduction / Context:
The phrase “as much greater than 31 as it is less than 55” means the number is equidistant from the two given values on the number line. Therefore, it must be the midpoint of 31 and 55. Finding midpoints is a common technique in arithmetic and algebra.

Given Data / Assumptions:

• The unknown number x satisfies x − 31 = 55 − x.
• All values are integers; solution can be non-integer in general, but here it turns out integral.
• Midpoint formula applies: midpoint = (a + b) / 2.

Concept / Approach:
Set the “greater than 31” difference equal to the “less than 55” difference. Solving this linear equation gives the midpoint directly. Alternatively, use the midpoint formula between 31 and 55 to reach the same result instantly.

Step-by-Step Solution:
1) Translate: x − 31 = 55 − x.2) Add x to both sides: 2x − 31 = 55.3) Add 31: 2x = 86.4) Divide by 2: x = 86 / 2 = 43.

Verification / Alternative check:
Midpoint method: (31 + 55) / 2 = 86 / 2 = 43. Differences check: 43 − 31 = 12 and 55 − 43 = 12, equal as required.

Why Other Options Are Wrong:
47 and 52 are not centered: their distances to 31 and 55 differ; 39 is closer to 31 than to 55; 42 is 11 away from 31 and 13 away from 55, not equal.

Common Pitfalls:
Subtracting the numbers instead of averaging; misreading the phrase and setting x − 31 = x − 55; arithmetic slips when dividing by 2.

Final Answer:
43