A rideshare company charges a fixed booking fee plus a constant per-mile rate. For a trip of m miles, the...

1. SIMPLIFY the equation to standard form

• Given equation: \(\mathrm{C - 1.25m = 3.50}\)
• Add 1.25m to both sides: \(\mathrm{C = 1.25m + 3.50}\)
• Now we have the standard linear form: \(\mathrm{C = (rate)(miles) + (fixed\ cost)}\)

2. INFER the meaning of each component

• In the equation \(\mathrm{C = 1.25m + 3.50}\):
  • 1.25 is the coefficient of m, so it's the per-mile rate ($1.25 per mile)
  • 3.50 is the constant term, so it's the cost when \(\mathrm{m = 0}\) (the fixed booking fee)

3. TRANSLATE back to the context

• The problem asks about the interpretation of 3.50
• Since 3.50 is the constant term in our linear cost model, it represents the fixed booking fee
• This fee is charged regardless of how many miles are driven

Answer: C

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY skills: Students fail to rearrange the equation into standard linear form (\(\mathrm{C = 1.25m + 3.50}\)) and instead try to interpret the original form directly.

Without rearranging, they might incorrectly think that since 1.25 and 3.50 are the only numbers in the equation, one must be the per-mile rate. This confusion may lead them to select Choice B (The per-mile rate is $3.50 per mile).

Second Most Common Error:

Poor INFER reasoning: Students rearrange correctly but don't connect the constant term to the fixed cost concept in linear models.

They might think 3.50 has some other meaning related to distance or special conditions, leading them to select Choice A (The per-mile rate begins after the car travels 3.50 miles) or get confused and guess.

The Bottom Line:

This problem tests whether students can work with linear equations in unfamiliar forms and connect algebraic structure to real-world meaning. The key insight is recognizing that rearranging reveals the standard cost model structure.