Approximation and quick calculation: Evaluate 30.9 × 3000 − 10.1 × 1100 + 8298 − 4302 and choose the closest option.

Difficulty: Easy

Correct Answer: 85000

Explanation:


Introduction / Context:
The expression combines two scaled products and a net constant adjustment. Compute each product exactly, apply the subtraction, add the constants, and pick the nearest large-rounded option.


Given Data / Assumptions:

  • 30.9 * 3000
  • 10.1 * 1100
  • + 8298 − 4302


Concept / Approach:
Perform the clean multiples first, then the smaller net constant. Because options are in 5000 increments, exact arithmetic directly identifies the closest value.


Step-by-Step Solution:

30.9 * 3000 = 92700 10.1 * 1100 = 11110 Difference so far = 92700 − 11110 = 81590 8298 − 4302 = 3996 Total = 81590 + 3996 = 85586 Closest option: 85000


Verification / Alternative check:
Rounding constants slightly (e.g., 3996 ≈ 4000) gives 81590 + 4000 = 85590, still closest to 85000 versus 90000.


Why Other Options Are Wrong:
80000 is 5586 low; 90000 is 4414 high; 105000 is far off.


Common Pitfalls:
Dropping a zero when multiplying by 3000 or 1100, which changes the result by orders of magnitude.


Final Answer:
85000

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