A factory produces electronic components at a constant rate. The equation below estimates the number of components n produced after...

1. TRANSLATE the equation information

• Given equation: \(\mathrm{n = 36h}\)
• Where \(\mathrm{n}\) = number of components produced
• Where \(\mathrm{h}\) = hours of operation
• Need to determine what 36 represents

2. INFER the mathematical relationship

• This is a linear equation in the form \(\mathrm{y = mx}\)
• The coefficient 36 is multiplied by \(\mathrm{h}\) (hours)
• Since \(\mathrm{n}\) (components) \(\mathrm{= 36 \times h}\) (hours), the 36 must have units that make this equation dimensionally correct

3. INFER the units and meaning

• \(\mathrm{n}\) has units of "components"
• \(\mathrm{h}\) has units of "hours"
• For the equation to be valid: \(\mathrm{components = 36 \times hours}\)
• Therefore, 36 must have units of "components per hour"
• This means 36 represents the production rate

Answer: C - The factory produces components at a rate of 36 per hour

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students focus on the number 36 itself rather than understanding its role as a coefficient in the linear equation.

They might think "36" refers to a total amount of something (like total components or batches) rather than recognizing it as a rate. This leads to confusion about whether 36 is the final answer or represents some quantity.

This may lead them to select Choice B (The total number of components produced is 36) or get confused and guess.

The Bottom Line:

Success on this problem requires understanding that coefficients in linear equations often represent rates of change, not just static quantities. The key insight is recognizing that 36 tells us "how many components per hour," not "how many components total."