PSAT Math Multiple-Choice Question 302: Answer and Explanation

Question: 302

Price of One Can	Projected Number of Cans Sold
$0.75	10,000
$0.80	9,000
$0.85	8,000
$0.90	7,000
$0.95	6,000
$1.00	5,000

Which of the following equations best describes the relationship shown in the table, where n indicates the number of cans sold and p represents the price in dollars of one can?

• A. n = -20,000p + 25,000
• B. n = -200p + 250
• C. n = 200p + 250
• D. n = 20,000p + 25,000

Correct Answer: A

Explanation:

A

Difficulty: Medium

Category: Linear Graphs

Getting to the Answer: The answer choices are given in slope-intercept form, so start by finding the slope. To do this, substitute two pairs of values from the table into the slope formula, . Keep in mind that the projected number of cans sold depends on the price, so the price is the independent variable (x) and the projected number is the dependent variable (y). Using the points (0.75, 10,000) and (1.0, 5,000), the slope is:

This means that (A) must be correct because it is the only one that has a slope of -20,000. Don't let (D) fool you—the projected number of cans sold goes down as the price goes up, so there is an inverse relationship, and the slope must be negative.