A line segment that has a length of 115 centimeters (cm) is divided into three parts. One part is 47...

1. TRANSLATE the problem information

• Given information:
  • Total segment length: 115 cm
  • One part: 47 cm
  • Two other parts: equal lengths (unknown)
  • Find: length of one equal part

• Let \(\mathrm{x}\) = length of each equal part

2. TRANSLATE into an equation

• The three parts must add up to the total length:
  \(\mathrm{47 + x + x = 115}\)

• This simplifies to: \(\mathrm{47 + 2x = 115}\)

3. SIMPLIFY by solving the equation

• Subtract 47 from both sides:
  \(\mathrm{2x = 115 - 47}\)
  \(\mathrm{2x = 68}\)

• Divide both sides by 2:
  \(\mathrm{x = 34}\)

Answer: 34

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students may misinterpret "the other two parts have lengths that are equal to each other" and set up an incorrect equation like \(\mathrm{47 + x = 115}\), forgetting there are actually THREE parts total.

This leads them to calculate \(\mathrm{x = 115 - 47 = 68}\), giving an incorrect answer of 68.

Second Most Common Error:

Poor SIMPLIFY execution: Students set up the correct equation \(\mathrm{47 + 2x = 115}\) but make arithmetic errors, such as calculating \(\mathrm{115 - 47 = 78}\) instead of 68, leading to \(\mathrm{x = 39}\) instead of the correct \(\mathrm{x = 34}\).

The Bottom Line:

This problem tests whether students can carefully parse the language about "three parts" where two are equal, then accurately translate that understanding into a solvable equation. The arithmetic itself is straightforward once the setup is correct.