What approximate value will come in place of the question mark (?) in the…

Concept

In approximation (simplification) problems, round each quantity to the nearest convenient value before computing, then solve for the unknown. A cube grows fast, so a small rounding of the base is the dominant simplification: round the base first, then cube it. The standard rounding here is 12.21 → 12, 108.02 → 108, and 24.90% of 399 → 25% of 400.

Application

1. Approximate the cube by rounding the base: 12.213 ≈ 123 = 1728.

2. Approximate the subtracted term: 108.02 ≈ 108.

3. Approximate the percentage: 24.90% of 399 ≈ 25% of 400 = 100.

4. Substitute into 12.213 − 108.02 = 24.90% of 399 + ? to get 1728 − 108 = 100 + ?.

5. Simplify the left side: 1728 − 108 = 1620, so 1620 = 100 + ?.

6. Solve for ?: ? = 1620 − 100 = 1520.

Cross-check

Reverse it: 100 + 1520 = 1620, and 1620 + 108 = 1728 = 123, which recovers the rounded left-hand side. Exact arithmetic gives 12.213 ≈ 1820.3 and 24.90% of 399 ≈ 99.35, so the unrounded value of ? is about 1613; the base-rounding 12.21 → 12 that this "approximate value" instruction expects lands on 1520, which is also by far the nearest of the values offered.