A neighborhood consists of a 2-hectare park and a 35-hectare residential area. The total number of trees in the neighborhood...

1. TRANSLATE the problem information

• Given information:
  • Park area: 2 hectares
  • Residential area: 35 hectares
  • Total neighborhood trees: 3,934
  • Equation representing situation: \(\mathrm{2x + 35y = 3,934}\)

2. INFER the equation structure

• The equation \(\mathrm{2x + 35y = 3,934}\) follows the pattern:
  \(\mathrm{(Area_1 \times Rate_1) + (Area_2 \times Rate_2) = Total}\)
• Since we know the areas (2 and 35) and total (3,934), the variables x and y must represent rates
• This means:
  • \(\mathrm{2x}\) = total trees in the park
  • \(\mathrm{35y}\) = total trees in residential area

3. INFER what x represents

• Since \(\mathrm{2x}\) gives the total trees in the park:
  • \(\mathrm{2\ hectares \times x\ trees\ per\ hectare = total\ park\ trees}\)
  • Therefore, \(\mathrm{x = trees\ per\ hectare\ in\ the\ park}\)

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

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students may focus on the numbers in the equation without connecting them to the real-world context. They might see "\(\mathrm{2x}\)" and think x represents the total trees in the park, not recognizing that 2 (the area) times x (the rate) equals the total.

This may lead them to select Choice C (The total number of trees in the park)

The Bottom Line:

This problem requires recognizing that variables in context problems often represent rates or densities, not just totals. The key insight is understanding that the equation structure (area × rate = total) determines what each variable means.