x + y = 350 The given equation relates the total number of maple trees, x, and the total number...

1. TRANSLATE the problem information

• Given information:
  • Equation relating trees: \(\mathrm{x + y = 350}\)
  • \(\mathrm{x}\) = total maple trees, \(\mathrm{y}\) = total birch trees
  • 245 maple trees were planted
  • Forest preserve is 14 acres (this is extra information)

• What we need to find: number of birch trees (\(\mathrm{y}\))

2. INFER the solution approach

• Since we know \(\mathrm{x = 245}\) and have the equation \(\mathrm{x + y = 350}\), we can substitute the known value to solve for the unknown
• Strategy: Use substitution method

3. SIMPLIFY through substitution and algebra

• Substitute \(\mathrm{x = 245}\) into the equation:

\(\mathrm{245 + y = 350}\)

• Solve for \(\mathrm{y}\) by subtracting 245 from both sides:

\(\mathrm{y = 350 - 245}\)
\(\mathrm{y = 105}\)

Answer: C. 105

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misread what quantity the question is asking for and select information that was given in the problem rather than what was asked.

Since the problem mentions "245 maple trees" and asks about birch trees, some students reflexively choose the maple tree count without solving. Others notice "14-acre forest preserve" and think this number might be relevant to the answer.

This may lead them to select Choice A (14) or Choice D (245)

Second Most Common Error:

Inadequate SIMPLIFY execution: Students set up the substitution correctly but make basic arithmetic errors when calculating \(\mathrm{350 - 245}\).

A calculation error like \(\mathrm{350 - 245 = 25}\) (perhaps confusing this with \(\mathrm{270 - 245}\)) leads to an incorrect result.

This may lead them to select Choice B (25)

The Bottom Line:

This problem tests whether students can extract the right information from a word problem and apply basic algebraic substitution without getting distracted by irrelevant details or making careless arithmetic mistakes.