A conference room has a total floor area of 850 square feet. The room must accommodate a presentation screen and...

1. TRANSLATE the problem information

• Given information:
  • Total conference room area: 850 square feet
  • Equipment occupies: 100 square feet
  • Each table requires: 20 square feet
  • Find: Maximum number of tables

2. INFER the approach

• We need to find usable space first, then see how many tables fit
• Strategy: Subtract occupied space, then divide by space per table

3. Calculate available space

• Available space = Total space - Equipment space
• Available space = \(\mathrm{850 - 100 = 750}\) square feet

4. SIMPLIFY to find maximum tables

• Maximum tables = Available space ÷ Space per table
• Maximum tables = \(\mathrm{750 \div 20 = 37.5}\)

5. APPLY CONSTRAINTS to select final answer

• Since we cannot have 37.5 tables (physical impossibility), we need a whole number
• We must round DOWN to 37 because 38 tables would require \(\mathrm{38 \times 20 = 760}\) square feet
• But we only have 750 square feet available, so 38 tables won't fit

Answer: B (37)

Why Students Usually Falter on This Problem

Most Common Error Path:

Poor APPLY CONSTRAINTS reasoning: Students calculate 37.5 correctly but then round to the nearest whole number (38) instead of considering the physical constraint.

They think: "37.5 is closer to 38, so the answer must be 38 tables." However, 38 tables would need 760 square feet, which exceeds the 750 available. Students who make this error don't verify their final answer against the space constraint.

This may lead them to select Choice C (38).

Second Most Common Error:

Weak TRANSLATE skill: Students misunderstand what space is actually available for tables and use the total room area (850) instead of the remaining area after equipment placement.

They calculate: \(\mathrm{850 \div 20 = 42.5}\), then round down to 42. This completely ignores that 100 square feet is unavailable due to equipment.

This may lead them to select Choice D (42).

The Bottom Line:

This problem tests whether students can properly handle real-world constraints in mathematical solutions. The key insight is that mathematical answers (like 37.5) must sometimes be adjusted based on physical reality, and that adjustment isn't always "round to the nearest whole number."