The cost to rent a commercial fishing boat from a certain company is $950 for the first 2 hours and...

1. TRANSLATE the pricing structure

• Given information:
  • \(\$950\) for the first 2 hours (fixed cost)
  • \(\$50\) per hour for each hour after the first 2 hours
  • Total cost for t hours is \(\$1,100\) (where \(\mathrm{t \gt 2}\))

2. INFER how to break down the cost components

• Since \(\mathrm{t \gt 2}\), we have two cost components:
  • Fixed cost: \(\$950\) (covers first 2 hours regardless of how many total hours)
  • Variable cost: depends on additional hours beyond the first 2
• Additional hours beyond first 2 = \(\mathrm{(t - 2)}\)

3. TRANSLATE the variable cost

• Cost for additional hours = \(\$50\) × (number of additional hours)
• Cost for additional hours = \(\$50 \times \mathrm{(t - 2)}\) = \(\mathrm{50(t - 2)}\)

4. INFER the total cost equation

• Total cost = Fixed cost + Variable cost
• Total cost = \(\mathrm{950 + 50(t - 2)}\)

5. Set up the equation

• Since total cost equals \(\$1,100\):
  \(\mathrm{950 + 50(t - 2) = 1,100}\)

Answer: C

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misinterpret the \(\$950\) as applying to each individual hour rather than as a flat rate for the first 2 hours combined.

They might think: "\(\$950\) per hour for first 2 hours, then \(\$50\) per hour after that." This leads them to create equations like \(\mathrm{950(t - 2) + 50t}\), incorrectly applying the \(\$950\) rate to the additional hours.

This may lead them to select Choice A (\(\mathrm{950(t - 2) + 50t = 1,100}\)).

Second Most Common Error:

Poor TRANSLATE reasoning: Students apply the additional \(\$50\)/hour rate to all t hours instead of just the additional hours beyond the first 2.

They correctly identify the \(\$950\) as a fixed cost but then think the \(\$50\) applies to every hour, creating: \(\mathrm{950 + 50(2t)}\) or similar variations.

This may lead them to select Choice D (\(\mathrm{950 + 50(2t) = 1,100}\)).

The Bottom Line:

The key challenge is carefully parsing the piecewise pricing structure—recognizing that different rates apply to different time periods, not different rates per hour throughout the entire rental period.