A veterinarian recommends that each day a certain rabbit should eat 25 calories per pound of the rabbit's weight, plus...

1. TRANSLATE the problem information

• Given information:
  • Rabbit should eat 25 calories per pound of weight each day
  • Plus an additional 11 calories each day
  • \(\mathrm{c}\) = total daily calories, \(\mathrm{x}\) = rabbit's weight in pounds

• What this tells us: We have a rate (25 calories per pound) plus a fixed amount (11 calories)

2. INFER the mathematical structure

• This describes a linear relationship: rate × input + constant
• The "25 calories per pound" becomes \(\mathrm{25x}\) when the rabbit weighs \(\mathrm{x}\) pounds
• The "additional 11 calories" gets added as \(\mathrm{+11}\)

3. TRANSLATE into equation form

• Calories from weight: \(\mathrm{25\ \text{calories/pound}\ \times x\ \text{pounds} = 25x\ \text{calories}}\)
• Additional calories: \(\mathrm{+11\ \text{calories}}\)
• Total: \(\mathrm{c = 25x + 11}\)

Answer: D. \(\mathrm{c = 25x + 11}\)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misinterpret which number goes with which part of the description, switching the coefficients and constant.

They read "25 calories per pound plus 11 additional calories" but incorrectly think the 11 goes with "per pound" and the 25 becomes the additional amount. This leads them to write \(\mathrm{c = 11x + 25}\).

This may lead them to select Choice C (\(\mathrm{c = 11x + 25}\)).

Second Most Common Error:

Poor TRANSLATE reasoning: Students incorrectly combine the 25 and 11 before setting up the equation.

They think "25 calories per pound plus 11 additional calories" means "36 calories per pound total," missing that the 11 calories is a fixed amount regardless of weight. This leads them to write \(\mathrm{c = 36x}\).

This may lead them to select Choice B (\(\mathrm{c = 36x}\)).

The Bottom Line:

The key challenge is carefully parsing the language to distinguish between the rate-based component (25 calories per pound) and the fixed component (11 additional calories). Students must resist the urge to combine numbers before understanding what each represents in the real-world context.