A candle burns at a constant rate. The height h, in centimeters, of the candle t minutes after it is...

1. TRANSLATE the problem information

• Given information:
  • Equation: \(\mathrm{h = 18 - 0.5t}\)
  • \(\mathrm{h}\) = height in centimeters
  • \(\mathrm{t}\) = minutes after lighting
  • Need height when \(\mathrm{t = 6}\) minutes

2. SIMPLIFY by substitution and evaluation

• Substitute \(\mathrm{t = 6}\) into the equation:
  \(\mathrm{h = 18 - 0.5(6)}\)

• Follow order of operations (multiplication first):
  \(\mathrm{h = 18 - 3}\)

• Complete the subtraction:
  \(\mathrm{h = 15}\)

Answer: B. 15

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY execution: Students make arithmetic errors during calculation

Many students correctly set up \(\mathrm{h = 18 - 0.5(6)}\) but then make computational mistakes. They might calculate \(\mathrm{0.5 \times 6 = 2.5}\) instead of 3, leading to \(\mathrm{h = 18 - 2.5 = 15.5}\). Or they might compute \(\mathrm{18 - 3 = 16}\) through careless subtraction.

This may lead them to select Choice A (12) if they miscalculate the multiplication, or other incorrect choices through various arithmetic errors.

Second Most Common Error:

Poor TRANSLATE reasoning: Students misunderstand what the variable t represents

Some students might think \(\mathrm{t = 6}\) means something other than "6 minutes after lighting," or they might substitute incorrectly by thinking they need to use a different value. This confusion about the problem setup can lead to using wrong substitution values.

This leads to confusion and guessing among the answer choices.

The Bottom Line:

This problem tests whether students can accurately perform function evaluation through substitution. Success requires careful attention to arithmetic details and clear understanding of what the variables represent in the real-world context.