Question

1. a school library is planning to add a reference section to their collection. the library can add no more than 20 books, and the librarian decided that the school could use a maximum of 16 dictionaries and a maximum of 9 thesauruses. dictionaries cost $15, and thesauruses cost $10. list the three constraints (not including x ≥ 0 and y ≥ 0).

Explanation:

Step1: Define Variables

Let \( x \) be the number of dictionaries and \( y \) be the number of thesauruses.

Step2: Total Books Constraint

The total number of books (dictionaries + thesauruses) is no more than 20, so \( x + y \leq 20 \).

Step3: Dictionaries Constraint

The number of dictionaries is at most 16, so \( x \leq 16 \).

Step4: Thesauruses Constraint

The number of thesauruses is at most 9, so \( y \leq 9 \).

Answer:

\( x + y \leq 20 \)

\( x \leq 16 \)

\( y \leq 9 \)