A landscaping company has a supply of 265 paving stones. An employee uses 40 of these stones for a small...

1. TRANSLATE the problem information

• Given information:
  • Total paving stones: 265
  • Stones used for patio: 40
  • Number of identical garden paths: 9
  • All remaining stones are used for the paths
  • Need to find: stones per path

2. INFER the solution approach

• This is a two-step problem:
  • First, find how many stones remain after building the patio
  • Then, divide those remaining stones equally among the 9 paths
• We cannot simply divide 265 by 9 because some stones were already used

3. SIMPLIFY through calculation

Step 1: Find remaining stones after patio construction
\(265 - 40 = 225\) stones remaining

Step 2: Divide remaining stones equally among paths
\(225 \div 9 = 25\) stones per path

Answer: C) 25

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students jump straight to dividing the total stones by the number of paths, forgetting to account for the patio stones first.

They calculate: \(265 \div 9 = 29.4...\) and round to the nearest whole number.

This may lead them to select Choice D (29).

Second Most Common Error:

Poor TRANSLATE reasoning: Students misinterpret "remaining stones" and include the patio stones in their final division, or they make arithmetic errors in the subtraction or division steps.

This causes confusion and may lead to selecting an incorrect answer choice or guessing.

The Bottom Line:

The key challenge is recognizing that this problem requires removing the patio stones from consideration before dividing the rest equally. Students who rush through without carefully reading "remaining stones are used" miss this crucial two-step structure.