A total of 165 people contributed to a charity event as either a donor or a volunteer. 130 people contributed...

1. TRANSLATE the problem information

• Given information:
  • Total people who contributed: 165
  • People who donated: 130
  • Find: People who volunteered

• Key phrase: "either a donor or a volunteer" tells us these are the only two ways to contribute

2. INFER the mathematical relationship

• Since everyone is categorized as either a donor OR a volunteer (no overlap, no other options):
  \(\mathrm{Total = Donors + Volunteers}\)
• We know Total and Donors, so we can solve for Volunteers

3. Set up and solve the equation

• \(\mathrm{165 = 130 + Volunteers}\)
• \(\mathrm{Volunteers = 165 - 130 = 35}\)

Answer: A. 35

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misread "either...or" as meaning they should add the given numbers together instead of recognizing the part-whole relationship.

Instead of seeing "Total = Part 1 + Part 2" and solving for the missing part, they think they need to combine 165 + 130 = 295. While this specific sum doesn't match any answer choice, this type of confusion about the problem structure can lead to guessing or selecting Choice D (330) if they somehow incorporate both numbers in their calculation.

Second Most Common Error:

Conceptual confusion about what the question asks: Students correctly identify that subtraction is needed but get confused about which number represents what they're looking for.

They might think "130 people contributed as donors, so that's how many volunteers there are" and select Choice B (130), or think "165 total people contributed, so that's the number of volunteers" and select Choice C (165).

The Bottom Line:

This problem tests whether students can correctly interpret "either...or" language as describing mutually exclusive categories that add up to a total, then apply basic algebra to find the missing piece.