Last month, a moving company charged customers according to the equation 55H + 90J = 6{,}785, where H is the...
GMAT Algebra : (Alg) Questions
Last month, a moving company charged customers according to the equation \(55\mathrm{H} + 90\mathrm{J} = 6{,}785\), where \(\mathrm{H}\) is the total number of labor hours worked across all jobs, \(\mathrm{J}\) is the number of jobs completed, and \(6{,}785\) is the total amount, in dollars, charged that month. Which of the following is the best interpretation of \(55\) in this context?
The company charged $55 per job that month.
The company worked 55 labor hours that month.
The company charged $55 per hour of labor that month.
The company completed 55 jobs that month.
1. TRANSLATE the equation structure
- Given equation: \(55\mathrm{H} + 90\mathrm{J} = 6,785\)
- Where:
- \(\mathrm{H}\) = total labor hours worked
- \(\mathrm{J}\) = number of jobs completed
- \(6,785\) = total charges in dollars
2. INFER the cost structure pattern
- This equation follows the format: (rate per unit)(units) + (rate per unit)(units) = total cost
- We need to identify what \(55\) represents by looking at what it multiplies
3. TRANSLATE the coefficient meanings
- \(55\) is the coefficient of \(\mathrm{H}\) (labor hours)
- \(90\) is the coefficient of \(\mathrm{J}\) (number of jobs)
- In cost equations, coefficients represent the rate or price per unit
4. INFER the final interpretation
- Since \(55\) multiplies \(\mathrm{H}\) (labor hours), \(55\) must be the charge per labor hour
- Since \(90\) multiplies \(\mathrm{J}\) (jobs), \(90\) must be the charge per job
Answer: C - The company charged $55 per hour of labor that month
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak TRANSLATE skill: Students confuse the coefficient (\(55\)) with the variable value (what \(\mathrm{H}\) equals)
They see '55' in the equation and think it represents either the actual number of hours worked or the actual number of jobs completed, rather than understanding it's the rate. This fundamental misunderstanding of algebraic structure leads them to select Choice B (The company worked 55 labor hours that month) or Choice D (The company completed 55 jobs that month).
Second Most Common Error:
Poor INFER reasoning about equation structure: Students don't recognize the standard cost equation pattern
They may understand that \(55\) is a coefficient but fail to connect it to the specific quantity it multiplies. Without recognizing that coefficients in cost equations represent rates, they might incorrectly associate \(55\) with jobs instead of labor hours. This may lead them to select Choice A ($55 per job).
The Bottom Line:
Success requires recognizing that in cost equations like this, each coefficient tells you the rate per unit for whatever quantity it multiplies. The key insight is that \(55 \times \mathrm{H}\) means '55 dollars per hour × number of hours.'
The company charged $55 per job that month.
The company worked 55 labor hours that month.
The company charged $55 per hour of labor that month.
The company completed 55 jobs that month.