Approximation and quick calculation: Solve 56.001 × ? − 1000.999 = 231. Find the closest integer value of ?.

Introduction / Context:
A single linear equation in one variable with coefficients near integers is ideal for quick isolation of the unknown. Since the options are integers, compute the value and select the nearest integer if needed.

Given Data / Assumptions:

• 56.001 * ? − 1000.999 = 231
• Find integer ? closest to the true value.

Concept / Approach:
Rearrange to ? = (231 + 1000.999) / 56.001. Note that the numerator is about 1231.999 and the denominator about 56, indicating a value near 22.

Step-by-Step Solution:

Verification / Alternative check:
Back-substitute 22: 56.001*22 − 1000.999 ≈ 1232.022 − 1000.999 ≈ 231.023, essentially exact within rounding, confirming the choice.

Why Other Options Are Wrong:
45, 37, 16 produce results far from 231 when back-substituted due to the large multiplier 56.001.

Common Pitfalls:
Using 56 instead of 56.001 is fine here; but do not forget to add 1000.999 to 231 before dividing, or you will subtract incorrectly.

Final Answer:
22