A certain elephant weighs 200 pounds at birth and gains more than 2 but less than 3 pounds per day...

1. TRANSLATE the problem information

• Given information:
  • Birth weight: 200 pounds
  • Daily weight gain: more than 2 pounds but less than 3 pounds per day
  • Time period: 365 days (first year)
  • Need to find: possible weights after 365 days

• What this tells us: We need to find a range of possible weights, not just one value.

2. TRANSLATE the weight relationship

• The elephant's weight after 365 days equals:
  Birth weight + (daily gain × number of days)

• Since the daily gain is between 2 and 3 pounds:
  \(\mathrm{w = 200 + (daily\ gain \times 365)}\), where \(\mathrm{2 \lt daily\ gain \lt 3}\)

• This creates the inequality: \(\mathrm{200 + (2 \times 365) \lt w \lt 200 + (3 \times 365)}\)

3. SIMPLIFY the arithmetic

• Calculate the lower bound: \(\mathrm{200 + (2 \times 365) = 200 + 730 = 930}\)

• Calculate the upper bound: \(\mathrm{200 + (3 \times 365) = 200 + 1095 = 1295}\)

• Final inequality: \(\mathrm{930 \lt w \lt 1{,}295}\)

Answer: D. \(\mathrm{930 \lt w \lt 1{,}295}\)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students confuse how to combine the birth weight with weight gains, thinking they should multiply the birth weight by the daily gain rates instead of adding the accumulated weight gain to the birth weight.

This incorrect reasoning: "The elephant weighs 200 pounds and gains 2-3 times that amount" leads to \(\mathrm{200(2) \lt w \lt 200(3)}\), giving \(\mathrm{400 \lt w \lt 600}\).

This may lead them to select Choice A (\(\mathrm{400 \lt w \lt 600}\)).

Second Most Common Error:

Poor TRANSLATE reasoning: Students misread the daily weight gain as "1-2 pounds" instead of "more than 2 but less than 3 pounds per day."

This gives them \(\mathrm{200 + (1 \times 365) \lt w \lt 200 + (2 \times 365)}\), resulting in \(\mathrm{565 \lt w \lt 930}\).

This may lead them to select Choice B (\(\mathrm{565 \lt w \lt 930}\)).

Third Error Path:

Incomplete TRANSLATE execution: Students correctly calculate the weight gained (730 to 1095 pounds) but forget to add the initial birth weight of 200 pounds.

This gives them just the weight gain range: \(\mathrm{730 \lt w \lt 1{,}095}\).

This may lead them to select Choice C (\(\mathrm{730 \lt w \lt 1{,}095}\)).

The Bottom Line:

This problem tests whether students can properly TRANSLATE a compound constraint (birth weight PLUS accumulated daily gains) into mathematical form, avoiding the trap of treating it as a simple multiplication problem.