Find the missing percentage: 39.8% of 400 + ?% of 350 = 230 (approximate to the nearest option).
Correct Answer: 20
Introduction / Context:This is a reverse-percentage problem. We compute the first term, subtract it from the total 230, and then back out the percentage of 350 that remains.Given Data / Assumptions:
- First term: 39.8% of 400.
- Second term: ?% of 350.
- Sum ≈ 230.
Concept / Approach:Compute the known percentage value, find the required remainder, convert that remainder to a percentage of 350, and finally select the nearest whole-number percentage from the options.Step-by-Step Solution:
39.8% of 400 = 0.398 × 400 = 159.2.Remainder needed = 230 − 159.2 = 70.8.Let x% of 350 ≈ 70.8 ⇒ (x/100) × 350 ≈ 70.8.x ≈ (70.8 / 350) × 100 ≈ 20.23%.Nearest listed percentage: 20%.Verification / Alternative check:Check: 20% of 350 = 70; total = 159.2 + 70 = 229.2, close to 230. Given approximation framing, 20% is the most reasonable choice.Why Other Options Are Wrong:
- 15%: Gives 52.5, too small.
- 18%: Gives 63, still small.
- 25%: Gives 87.5, too large.
Common Pitfalls:Mixing bases (e.g., applying the second percentage to 400 instead of 350) or forgetting to convert the percentage remainder correctly. Always identify the correct base for each percentage.Final Answer:
20