Question

Abby works at a car dealership and receives a commission "c" which is a percent of the profit the dealership makes from the sale, which is the difference between the price "p" of the car and the value "v" of the car. How much, in dollars, does the dealership earn per transaction?

• A. \((p - v)(0.01c)\)
• B. \((p - v)(1 - 0.01c)\)
• C. \(p(v - 0.01c)\)
• D. \((p - v)(1 - c)\)
• E. \(pv(0.01c)\)

Hint:

Be very careful with how percentages are defined. If a variable 'c' is "a percent," it means the number itself (e.g., c=10 for 10%). To use it in multiplication, you must convert it to a decimal (c/100 or 0.01c). This is a common trap in percentage problems.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
This is a problem about calculating profit and commission. We need to translate the verbal description into a mathematical expression. The dealership's earning is the total profit from the sale minus the commission paid to the salesperson.
Step 2: Key Formula or Approach:
1. Define the profit. 2. Define the commission amount paid to Abby. 3. Define the dealership's earnings as Profit - Commission. 4. Simplify the resulting expression.
Step 3: Detailed Explanation:
The profit from the sale is the difference between the price (p) and the value (v): \[ \text{Profit} = p - v \] Abby's commission "c" is a percent of the profit. To use it in a calculation, we must convert the percentage to a decimal by dividing by 100. \[ \text{Commission Amount} = \frac{c}{100} \times \text{Profit} = 0.01c \times (p - v) \] The dealership's earning is the total profit minus the commission they pay to Abby: \[ \text{Dealership Earns} = \text{Profit} - \text{Commission Amount} \] \[ \text{Dealership Earns} = (p - v) - 0.01c(p - v) \] We can factor out the common term \((p - v)\): \[ \text{Dealership Earns} = (p - v)(1 - 0.01c) \] Step 4: Final Answer:
The expression for the dealership's earnings is \((p - v)(1 - 0.01c)\).