To qualify for the honor society, a student must accumulate at least 240 service points. Jamie currently has 187 service...

1. TRANSLATE the problem information

• Given information:
  • Jamie currently has 187 service points
  • Needs at least 240 points to qualify
  • Each additional event gives 9 points
  • Find minimum number of additional events

2. TRANSLATE the constraint into mathematics

• Jamie's total after n additional events: \(187 + 9\mathrm{n}\)
• This must be at least 240: \(187 + 9\mathrm{n} \geq 240\)

3. SIMPLIFY to solve for n

• Subtract 187 from both sides: \(9\mathrm{n} \geq 240 - 187\)
• Calculate the difference: \(9\mathrm{n} \geq 53\)
• Divide by 9: \(\mathrm{n} \geq 53/9\)
• Calculate the decimal (use calculator): \(\mathrm{n} \geq 5.888...\)

4. APPLY CONSTRAINTS to find the minimum whole number

• Since Jamie can't attend partial events, n must be a whole number
• Since we need \(\mathrm{n} \geq 5.888...\), the minimum whole number is 6

5. Verify the answer

• With 6 events: \(187 + (6 \times 9) = 187 + 54 = 241 \geq 240\) ✓
• With 5 events: \(187 + (5 \times 9) = 187 + 45 = 232 \lt 240\) ✗

Answer: B (6)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak APPLY CONSTRAINTS skill: Students calculate \(53 \div 9 = 5.888...\) and incorrectly round down to 5 instead of up to 6.

They think "5.888 is close to 6, so 5 should be enough" without checking if 5 events actually meets the requirement. When they calculate \(187 + (5 \times 9) = 232\), they don't recognize that \(232 \lt 240\) means Jamie doesn't qualify.

This may lead them to select Choice A (5).

Second Most Common Error:

Poor TRANSLATE reasoning: Students misinterpret "at least 240" and set up the equation \(187 + 9\mathrm{n} = 240\) instead of the inequality \(187 + 9\mathrm{n} \geq 240\).

This gives them \(\mathrm{n} = 53/9 = 5.888...\), and since they can't have a fractional event, they might think the problem has no solution or round to the nearest whole number without understanding they need to ensure the minimum requirement is met.

This leads to confusion and guessing among the answer choices.

The Bottom Line:

This problem requires recognizing that "minimum" problems with "at least" constraints need you to round UP to the next whole number, not just to the nearest whole number. The mathematical solution gives you the boundary, but real-world constraints determine the final answer.