T = 1,000 + 18h In the equation above, T represents Brittany's total take-home pay, in dollars, for her first...

1. TRANSLATE the problem information

• Given information:
  • \(\mathrm{T = 1,000 + 18h}\) (equation relating total pay to hours worked)
  • \(\mathrm{T = \$1,576}\) (Brittany's actual total take-home pay)
  • Need to find: \(\mathrm{h}\) (hours worked)

2. TRANSLATE the key substitution

• Since Brittany's total take-home pay was $1,576, we can substitute \(\mathrm{T = 1,576}\) into our equation:
  \(\mathrm{1,576 = 1,000 + 18h}\)

3. SIMPLIFY to isolate the variable

• Subtract 1,000 from both sides:
  \(\mathrm{1,576 - 1,000 = 18h}\)
  \(\mathrm{576 = 18h}\)

• Divide both sides by 18:
  \(\mathrm{h = 576 \div 18 = 32}\)

Answer: B. 32

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY execution: Making arithmetic errors during calculation steps.

Students might incorrectly calculate 1,576 - 1,000 or make division errors with 576 ÷ 18. Some students also get confused and divide the wrong numbers together, like dividing 1,576 by 18 directly (which gives approximately 87.6, leading them toward Choice D (88)) or dividing 1,000 by 18 (which gives approximately 55.6, leading them toward Choice C (55)).

Second Most Common Error:

Poor TRANSLATE reasoning: Misunderstanding which value to substitute for T.

Students might get confused about what the $1,576 represents in the context of the equation, or they might try to work backwards from the answer choices rather than using the substitution method systematically. This leads to confusion and guessing.

The Bottom Line:

This problem tests whether students can connect word problem information to algebraic equations through substitution, then execute clean algebraic steps. The key insight is recognizing that when you're told a specific value for a variable, you substitute that value directly into the equation.