PSAT Math Multiple-Choice Question 15: Answer and Explanation

Question: 15

Ann is writing a book that will include up to 98 recipes. She currently has 32 main dish recipes and 18 dessert recipes. If r represents the number of additional recipes that Ann could include in her book, which of the following inequalities represents all possible values of r?

• A. r - 50 ≥ 98
• B. r - 50 ≤ 98
• C. 98 - (32 + 18) - r ≤ 0
• D. 98 - (32 + 18) - r ≥ 0

Correct Answer: D

Explanation:

D

The question asks for an inequality that represents all values of r. Translate the question in Bite-Sized Pieces, and use Process of Elimination. The total number of recipes Ann will include in her book is the sum of 32 main dish recipes, 18 dessert recipes, and r additional recipes. The book will include up to 98 recipes, meaning the greatest possible number of recipes in the book is 98. This information can be written as the inequality 32 + 18 + r ≤ 98. Subtract 32 and 18 from both sides to get r ≤ 48. Isolate r in the answer choices to find the one that matches r ≤ 48. For (A), add 50 to both sides to get r ≥ 148. Eliminate (A). For (B), add 50 to both sides to get r ≤ 148. Eliminate (B). For (C), add r to both sides to get 98 - (32 + 18) < r, which becomes 48 < r. Eliminate (C). For (D), add r to both sides to get 98 -(32 + 18) ≥ r, which becomes 48 ≥ r. The correct answer is (D).