A candle is made of 17 ounces of wax. When the candle is burning, the amount of wax in the...

1. TRANSLATE the problem information

• Given information:
  • Candle starts with 17 ounces of wax
  • Burns at rate of 1 ounce every 4 hours
  • Currently has 6 ounces remaining
  • Need to find: total hours of burning

2. INFER what we need to find first

• To use the burning rate, we first need to know how much wax has been consumed
• The consumed amount = original amount - remaining amount

3. Calculate wax consumed

• Wax consumed = \(17 - 6 = 11\) ounces

4. INFER how to apply the rate

• If 1 ounce burns in 4 hours, then 11 ounces will burn in 11 times as long
• This gives us: \(\mathrm{11}\) ounces \(\times\) \(\mathrm{4}\) hours/ounce

5. SIMPLIFY to find total time

• Total time = \(11 \times 4 = 44\) hours

Answer: D. 44

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students might confuse what the "6 ounces" represents and try to work directly with the remaining wax instead of the consumed wax.

They might set up something like: \(\mathrm{6}\) ounces \(\times\) \(\mathrm{4}\) hours/ounce \(= 24\) hours, thinking this represents the burning time. This leads them to select Choice C (24).

Second Most Common Error:

Incomplete INFER reasoning: Students recognize they need to find consumed wax (11 ounces) but then incorrectly think: "If it takes 4 hours to burn 1 ounce, then it takes \(\frac{11}{4}\) hours to burn 11 ounces."

This backward reasoning leads to \(11 \div 4 = 2.75 \approx 3\) hours, causing them to select Choice A (3).

The Bottom Line:

This problem tests whether students can correctly identify what quantity to work with (consumed wax, not remaining wax) and properly apply rate relationships in the forward direction (more ounces = more time, not less time).