An online bookstore sells novels and magazines. Each novel sells for $4, and each magazine sells for $1. If Sadie...

1. TRANSLATE the problem information

• Given information:
  • Novels cost \(\$4\) each, magazines cost \(\$1\) each
  • Total items purchased = 11
  • Total money spent = \(\$20\)
  • Need to find: number of novels

2. TRANSLATE into mathematical equations

• Let \(\mathrm{n}\) = number of novels, \(\mathrm{m}\) = number of magazines
• From "total of 11 items": \(\mathrm{n + m = 11}\)
• From "combined price of \(\$20\)": \(\mathrm{4n + m = 20}\)

3. INFER the solution approach

• This is a system of two equations with two unknowns
• Elimination method works well since both equations have "m" with coefficient 1

4. SIMPLIFY using elimination

• Subtract equation 1 from equation 2:
  \(\mathrm{(4n + m) - (n + m) = 20 - 11}\)
  \(\mathrm{3n = 9}\)
  \(\mathrm{n = 3}\)

5. Verify the answer

• If \(\mathrm{n = 3}\), then \(\mathrm{m = 11 - 3 = 8}\)
• Cost check: \(\mathrm{3(\$4) + 8(\$1) = \$20}\) ✓

Answer: B. 3

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students may set up incorrect equations, such as mixing up which variable represents which item, or incorrectly translating "total of 11" into something like \(\mathrm{n + m = 20}\).

This leads to a completely wrong system of equations and may cause them to select any answer choice through faulty reasoning.

Second Most Common Error:

Poor SIMPLIFY execution: Students correctly set up the system but make algebraic errors when eliminating variables, such as \(\mathrm{4n - n = 4n}\) instead of \(\mathrm{3n}\), or adding instead of subtracting equations.

This may lead them to select Choice A (2) or Choice C (4) depending on the specific calculation error.

The Bottom Line:

This problem tests whether students can systematically convert a real-world constraint problem into mathematics and solve methodically. Success requires careful translation and systematic algebraic manipulation.