PSAT Math Multiple-Choice Question 303: Answer and Explanation

Question: 303

A freight company charges a flat insurance fee to deliver a package anywhere in the continental United States, plus an additional charge for each pound the package weighs. The graph shows the relationship between the weight of the package and the total cost to ship it. Based on the graph, how much would it cost to ship a 25-pound box?

• A. $37.00
• B. $48.00
• C. $62.50
• D. $74.50

Correct Answer: D

Explanation:

D

Difficulty: Hard

Category: Linear Graphs

Getting to the Answer: In a real-world scenario, the y-intercept of a graph usually represents a flat fee or an initial value. The slope of the line represents a unit rate, such as the cost per pound. The y-intercept of the graph is 12, so the flat fee is $12. To find the cost per pound (the unit rate), substitute two points from the graph into the slope formula. Using the points (0, 12) and (2, 17), the unit rate is , which means $2.50 per pound will be added to the cost. The total cost to ship a 25-pound box is $12 + 2.50(25) = $12 + $62.50 = $74.50, which is (D).