PSAT Math Multiple-Choice Question 496: Answer and Explanation

Question: 496

Jean calculates how much money she spends on her dog Patches, and the results are shown below.

Expenses for Patches

Expense	Average Cost
dog food	$20 per week
dog walker	$30 per week

On top of these costs, Jean also pays an annual municipal licensing fee of $55. The cost, P, of caring for Patches for a given number of weeks, w, in the year can be calculated using the equation P = 55 + (20 + 30)w. When this function is graphed in the xy-plane, what does the slope represent?

• A. The cost of food and dog-walking per week
• B. The cost of licensing and food for a year
• C. The total cost of care per week
• D. The cost of licensing for a year

Correct Answer: A

Explanation:

A

The question asks about the graph of the data representing a certain situation. Label the parts of the equation to determine what they represent. In this question, P represents the cost of caring for Patches for a given number of weeks, and w represents the number of weeks. The equation is not quite in y = mx + b form, where m is the slope of a graph, but it can be rewritten as P = (20 + 30)w + 55. In this form, the slope is (20 + 30). According to the table, 20 and 30 represent the cost of dog food per week and the cost of dog walking per week, respectively. Only (A) reflects this. The correct answer is (A).