The total revenue from sales of a product can be calculated using the formula T = PQ, where T is...

1. TRANSLATE the problem information

• Given information:
  • Formula: \(\mathrm{T = PQ}\)
  • T represents total revenue
  • P represents price
  • Q represents quantity sold

• What we need: An equation that gives Q in terms of P and T

2. SIMPLIFY to isolate the variable Q

• Starting equation: \(\mathrm{T = PQ}\)
• To get Q by itself, divide both sides by P:
  \(\mathrm{\frac{T}{P} = \frac{PQ}{P}}\)
• The P's cancel on the right side:
  \(\mathrm{\frac{T}{P} = Q}\)
• Rearranging: \(\mathrm{Q = \frac{T}{P}}\)

Answer: B. \(\mathrm{Q = \frac{T}{P}}\)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY execution: Students get confused about which direction to divide and end up with the fraction upside down.

When dividing \(\mathrm{T = PQ}\) by P, they might incorrectly think "P goes on top" and write \(\mathrm{Q = \frac{P}{T}}\) instead of \(\mathrm{Q = \frac{T}{P}}\). This algebraic error stems from not carefully tracking which variable they're dividing by and where it should end up in the final fraction.

This leads them to select Choice A (\(\mathrm{Q = \frac{P}{T}}\)).

Second Most Common Error:

Conceptual confusion about algebraic operations: Students might think they need to multiply rather than divide to isolate Q.

Starting with \(\mathrm{T = PQ}\), they incorrectly reason "to get Q alone, I need to do something with P" and end up multiplying both sides by P instead of dividing, giving \(\mathrm{T \times P = Q}\), or \(\mathrm{Q = PT}\).

This may lead them to select Choice C (\(\mathrm{Q = PT}\)).

The Bottom Line:

This problem tests fundamental equation-solving skills. The key insight is recognizing that when a variable appears as part of a product (PQ), you isolate it by dividing both sides by the other factor (P), not by multiplying or subtracting.