The equation h = 24 + 2.5t gives the height h, in inches, of water in a tank t minutes...

1. TRANSLATE the problem information

• Given information:
  • Equation: \(\mathrm{h = 24 + 2.5t}\) (height formula)
  • At some point: height = 44 inches
  • Need to find: how many minutes (t)

2. TRANSLATE the height condition into mathematical form

• "The height of water in the tank was 44 inches" means \(\mathrm{h = 44}\)
• Now we have: \(\mathrm{44 = 24 + 2.5t}\)

3. SIMPLIFY to solve for t

• Subtract 24 from both sides:
  \(\mathrm{44 - 24 = 24 + 2.5t - 24}\)
  \(\mathrm{20 = 2.5t}\)

• Divide both sides by 2.5:
  \(\mathrm{t = 20 ÷ 2.5 = 8}\)

Answer: A. 8

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY execution: Students make arithmetic errors when dividing 20 by 2.5. Some might incorrectly calculate this as 10 (perhaps thinking \(\mathrm{20 ÷ 2 = 10}\)) or get confused by the decimal division.

This may lead them to select Choice B (10).

Second Most Common Error:

Poor TRANSLATE reasoning: Students might misunderstand which variable represents what they're solving for, or set up the wrong equation by confusing what equals 44. Some might incorrectly think they need to substitute t = 44 instead of h = 44.

This leads to confusion and abandoning the systematic solution, resulting in guessing among the answer choices.

The Bottom Line:

This problem tests whether students can properly connect word descriptions to mathematical symbols and then execute basic algebraic operations accurately. The key insight is recognizing that "height was 44 inches" directly translates to substituting \(\mathrm{h = 44}\) into the given equation.