A certain township consists of a 5-hectare industrial park and a 24-hectare neighborhood. The total number of trees in the...

1. TRANSLATE the problem information

• Given information:
  • 5-hectare industrial park
  • 24-hectare neighborhood
  • Total trees in township: 4,529
  • Equation: \(5\mathrm{x} + 24\mathrm{y} = 4,529\)

• What this tells us: The equation must represent how the total trees are distributed across the two areas.

2. INFER what the equation structure means

• Since the equation equals 4,529 (total trees), the left side must show how trees are distributed
• The equation has the form: (5 × something) + (24 × something) = total
• This suggests: \(5\mathrm{x}\) = trees in industrial park, \(24\mathrm{y}\) = trees in neighborhood

3. INFER what x specifically represents

• If \(5\mathrm{x}\) = total trees in the 5-hectare industrial park
• Then \(\mathrm{x}\) = (total trees in industrial park) ÷ 5 hectares
• This means \(\mathrm{x}\) = trees per hectare in the industrial park
• In other words, \(\mathrm{x}\) = average number of trees per hectare in industrial park

Answer: A. The average number of trees per hectare in the industrial park

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students may confuse which variable goes with which area, thinking x represents something about the neighborhood instead of the industrial park.

Since the equation shows \(5\mathrm{x}\) (and the industrial park is 5 hectares), students might incorrectly associate x with the 24-hectare neighborhood because it's mentioned second in the problem. This confusion about the variable-to-area correspondence may lead them to select Choice B (The average number of trees per hectare in the neighborhood).

Second Most Common Error:

Poor INFER reasoning: Students recognize that x goes with the industrial park but think x represents the total number of trees there rather than the per-hectare average.

They might reason "\(5\mathrm{x}\) means something about 5 hectares, so x must be the total trees in the industrial park." This misunderstanding of how multiplication works in context equations may lead them to select Choice C (The total number of trees in the industrial park).

The Bottom Line:

This problem requires students to understand that in context equations like this, when you multiply a rate by a quantity, the variable represents the rate (trees per hectare), not the total amount.