A moving company charges according to the equation C = 49 + 1.20w, where C is the total cost, in...

1. TRANSLATE the problem information

• Given information:
  • Cost equation: \(\mathrm{C = 49 + 1.20w}\)
  • \(\mathrm{C}\) = total cost in dollars
  • \(\mathrm{w}\) = weight in pounds
  • 49 = flat service fee charged once per shipment
  • Need to find: charge per pound

2. INFER what each part of the equation means

• In the linear equation \(\mathrm{C = 49 + 1.20w}\):
  • 49 is the fixed cost (doesn't depend on weight)
  • \(\mathrm{1.20w}\) is the variable cost (depends on weight)
  • The coefficient 1.20 tells us how much the cost increases for each additional pound

3. INFER the relationship between coefficient and rate

• Since \(\mathrm{w}\) represents pounds, and 1.20 is multiplied by \(\mathrm{w}\):
  • For 1 pound: cost increases by \(\mathrm{1.20 × 1 = \$1.20}\)
  • For 2 pounds: cost increases by \(\mathrm{1.20 × 2 = \$2.40}\)
  • Therefore, 1.20 represents the charge per pound

4. Eliminate incorrect choices

• Choice B (49): This is the flat fee, not per pound
• Choice C (\(\mathrm{1.20w}\)): This is the total variable cost for \(\mathrm{w}\) pounds, not the rate per pound
• Choice D (\(\mathrm{49 + 1.20w}\)): This is the entire cost equation, not just per pound

Answer: A (1.20)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students confuse the total variable cost with the per-unit rate. They see \(\mathrm{1.20w}\) and think "this involves both the rate AND the pounds, so this must be the per-pound charge." However, \(\mathrm{1.20w}\) represents the total cost for \(\mathrm{w}\) pounds, not the cost per individual pound.

This may lead them to select Choice C (\(\mathrm{1.20w}\))

Second Most Common Error:

Incomplete INFER reasoning: Students recognize that something in the equation represents per-pound cost but don't properly analyze what "per pound" means. They might think the flat fee somehow relates to per-pound charging or get confused about which component represents the rate.

This leads to confusion and guessing between the remaining choices.

The Bottom Line:

This problem tests whether students understand that in linear rate equations, the coefficient of the variable represents the unit rate. The key insight is distinguishing between the rate itself (1.20) and the total variable cost calculated using that rate (\(\mathrm{1.20w}\)).