A store sets the sale price s of a jacket to be 18 dollars less than its original price p....

1. TRANSLATE the problem statement

• Given information:
  • Sale price \(\mathrm{s}\) is 18 dollars less than original price \(\mathrm{p}\)
  • Need to express \(\mathrm{p}\) in terms of \(\mathrm{s}\)

• What "18 dollars less than" means:If something is "18 less than \(\mathrm{p}\)," we write it as \(\mathrm{p - 18}\)

2. TRANSLATE the relationship into an equation

• "Sale price \(\mathrm{s}\) is 18 dollars less than original price \(\mathrm{p}\)"
• This gives us: \(\mathrm{s = p - 18}\)

3. SIMPLIFY by solving for p

• Starting equation: \(\mathrm{s = p - 18}\)
• Add 18 to both sides: \(\mathrm{s + 18 = p - 18 + 18}\)
• Simplify the right side: \(\mathrm{s + 18 = p}\)
• Rewrite: \(\mathrm{p = s + 18}\)

Answer: B

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misinterpret "18 dollars less than original price \(\mathrm{p}\)"

Many students think "18 less than \(\mathrm{p}\)" means "\(\mathrm{18 - p}\)" instead of "\(\mathrm{p - 18}\)". This leads them to write \(\mathrm{s = 18 - p}\) instead of \(\mathrm{s = p - 18}\). When they solve this incorrect equation for \(\mathrm{p}\), they get \(\mathrm{p = 18 - s}\), which doesn't match any answer choice, leading to confusion and guessing.

Second Most Common Error:

Poor SIMPLIFY execution: Students set up the correct equation \(\mathrm{s = p - 18}\) but make an algebraic error when solving

They might subtract 18 from both sides instead of adding 18, getting \(\mathrm{s - 18 = p}\), which leads them to select Choice A (\(\mathrm{p = s - 18}\)).

The Bottom Line:

This problem tests whether students can accurately translate everyday language into mathematical relationships. The phrase "18 less than" is the critical translation challenge - students must recognize this means "subtract 18 from," not "18 minus."