Find the missing percentage: 39.8% of 400 + ?% of 350 = 230 (approximate to the nearest option).

Difficulty: Easy

Correct Answer: 20

Explanation:


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

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