A personal trainer recommends that during exercise, a client should burn 15 calories per minute of activity, plus a baseline...

1. TRANSLATE the problem information

• Given information:
  • 15 calories per minute of activity
  • 45 calories baseline metabolic burn during exercise session
  • c = total calories, t = time in minutes

• What this tells us: We have a rate (per minute) and a constant amount

2. TRANSLATE each component separately

• Activity calories: \(15 \text{ calories/minute} \times \mathrm{t} \text{ minutes} = 15\mathrm{t} \text{ calories}\)
• Baseline calories: 45 calories (stays the same regardless of time)

3. INFER how to combine the components

• Total calories = Activity calories + Baseline calories
• This creates: \(\mathrm{c} = 15\mathrm{t} + 45\)

Answer: C

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students mix up which number is the rate and which is the constant.

They might think "45 calories during exercise" means 45 calories per minute, leading to \(\mathrm{c} = 45\mathrm{t} + 15\). This represents 45 calories per minute plus a 15-calorie baseline, which reverses the actual situation.

This may lead them to select Choice D (\(\mathrm{c} = 45\mathrm{t} + 15\))

Second Most Common Error:

Incomplete TRANSLATE reasoning: Students correctly identify 15 calories per minute but forget to include the baseline burn.

They focus only on the activity component and write \(\mathrm{c} = 15\mathrm{t}\), missing that there's an additional 45 calories burned regardless of exercise duration.

This may lead them to select Choice A (\(\mathrm{c} = 15\mathrm{t}\))

The Bottom Line:

Word problems about rates require carefully distinguishing between per-unit amounts (which become coefficients of variables) and constant amounts (which become standalone terms in the equation).