The given equation t/2 = 5i + p relates the total baking time t, number of ingredients i, and preparation...

1. TRANSLATE the problem information

• Given equation: \(\mathrm{t/2 = 5i + p}\)
• Goal: Express t in terms of i and p (isolate t)

2. INFER the solution strategy

• Since t is divided by 2, I need to eliminate that fraction
• Strategy: Multiply both sides by 2 to isolate t

3. SIMPLIFY through algebraic manipulation

• Multiply both sides by 2:
  • Left side: \(\mathrm{(t/2) \times 2 = t}\)
  • Right side: \(\mathrm{(5i + p) \times 2 = 2(5i + p)}\)
• Result: \(\mathrm{t = 2(5i + p)}\)

Answer: A

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Not recognizing the basic strategy for solving equations with fractions. Students might stare at \(\mathrm{t/2 = 5i + p}\) and not immediately see that multiplying both sides by 2 will isolate t. Instead, they might try more complex approaches or get confused about which operation to perform.

This leads to confusion and guessing among the answer choices.

Second Most Common Error:

Poor SIMPLIFY execution: Students understand they need to multiply by 2, but make algebraic mistakes. They might incorrectly think that multiplying the right side by 2 changes the signs, leading them to write \(\mathrm{t = 2(5i - p)}\) instead of \(\mathrm{t = 2(5i + p)}\).

This may lead them to select Choice B (\(\mathrm{t = 2(5i - p)}\)).

The Bottom Line:

This problem tests the fundamental skill of isolating variables in linear equations. Success requires both recognizing the straightforward strategy (multiply by 2) and executing it without sign errors.