In North America, the standard width of a parking space is at least 7.5 feet and no more than 9.0...

1. TRANSLATE the problem setup

• Given information:
  • Parking space width: between 7.5 and 9.0 feet
  • Curb length: 135 feet
  • Spaces placed perpendicular to curb

• What this tells us: Since spaces are perpendicular to the curb, each space's width determines how much of the 135-foot curb it occupies

2. INFER the strategy for finding the range

• Key insight: We need both the minimum and maximum possible number of spaces
• To get the maximum number of spaces → use the minimum space width
• To get the minimum number of spaces → use the maximum space width

3. Calculate the maximum number of spaces

• Use minimum width: \(135 \div 7.5 = 18\) spaces maximum

4. Calculate the minimum number of spaces

• Use maximum width: \(135 \div 9 = 15\) spaces minimum

5. APPLY CONSTRAINTS to establish the complete range

• The number of spaces n must satisfy: \(15 \leq \mathrm{n} \leq 18\)

Answer: D. \(15 \leq \mathrm{n} \leq 18\)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students may not properly interpret "perpendicular to curb" and might confuse which dimension (width vs length) determines how many spaces fit along the curb.

This confusion could lead them to use the curb length (135) as an upper bound for the number of spaces, causing them to select Choice A (\(18 \leq \mathrm{n} \leq 135\)) or Choice C (\(15 \leq \mathrm{n} \leq 135\)).

Second Most Common Error:

Incomplete INFER reasoning: Students might only calculate one scenario (either minimum or maximum spaces) instead of recognizing they need both endpoints to establish the complete range.

This partial analysis might lead them to select Choice B (\(7.5 \leq \mathrm{n} \leq 9\)), mistakenly thinking the answer should reflect the width constraints rather than the number of spaces.

The Bottom Line:

This problem tests whether students can properly set up range problems by understanding the inverse relationship between individual item size and total quantity that fits in a fixed space.