Approximation and quick calculation: Evaluate (724 ÷ 25) × 31.05 + 101 and choose the closest option.

Introduction / Context:Convert the division by 25 to a multiplication by 4/100 for quicker mental math: dividing by 25 equals multiplying by 0.04. Then scale by 31.05 and add 101. Options are in the hundreds, so a tight estimate suffices.

Given Data / Assumptions:

• (724 / 25) * 31.05 + 101

Concept / Approach:First compute 724/25 exactly as 28.96. Multiply by 31.05, then add 101 and pick the nearest hundred-level option.

Step-by-Step Solution:

Verification / Alternative check:Even if 31.05 were rounded to 31, product 28.96*31 = 897.76; add 101 = 998.76 still closest to 1000.

Why Other Options Are Wrong:900 and 950 are too low; 1050 is too high. 1000 is closest to ~1000.21.

Common Pitfalls:Approximating 724/25 as 29 without adjusting can push the result slightly higher, but the nearest option remains 1000.

Final Answer:1000