A car rental company states that the maximum possible daily cost c, in dollars, depends on the number of rental...

1. TRANSLATE the key phrase into mathematical notation

• Given information:
  • "The maximum possible value of c is 9 more than 5 times h"

• TRANSLATE "9 more than 5 times h":
  • Start with "5 times h" = \(5\mathrm{h}\)
  • Add 9 to get: \(5\mathrm{h} + 9\)

2. INFER what "maximum possible value" means for the inequality

• If the maximum possible value of c is \(5\mathrm{h} + 9\), this sets an upper bound
• The daily cost c cannot exceed this maximum
• Therefore: \(\mathrm{c} \leq 5\mathrm{h} + 9\)

3. Match with the answer choices

Looking at the options, choice (B) \(\mathrm{c} \leq 5\mathrm{h} + 9\) matches our result exactly.

Answer: B

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students misunderstand what "maximum possible value" implies about the inequality direction.

They might think: "If the maximum possible value of c is \(5\mathrm{h} + 9\), then c must be at least that much," leading them to write \(\mathrm{c} \geq 5\mathrm{h} + 9\).

This reasoning confuses "maximum" with "minimum" and leads them to select Choice A (\(\mathrm{c} \geq 5\mathrm{h} + 9\)).

Second Most Common Error:

Poor TRANSLATE execution: Students mistranslate "9 more than 5 times h" as \(9 - 5\mathrm{h}\) instead of \(5\mathrm{h} + 9\).

This word order confusion (thinking "9 more than [something]" means "9 minus [something]") would lead them to \(\mathrm{c} \leq 9 - 5\mathrm{h}\).

This causes them to select Choice D (\(\mathrm{c} \leq 9 - 5\mathrm{h}\)).

The Bottom Line:

This problem tests whether students can correctly interpret constraint language ("maximum possible value") and translate mathematical phrases in the right order. Success requires both accurate translation and logical reasoning about what maximum values mean for inequalities.