Question

gwen is organizing a book drive at her school for martin luther king jr. day. she has 8 full boxes of books and 4 half - full boxes. each full box holds the same number of books and each half - full box holds half that amount. she also has 23 books that are not in any boxes. gwen has a total of 363 books. use x to represent the number of books in a full box. write an equation to represent the situation. use the number pad and x to enter your answer in the box. \boxed{} = 363

Explanation:

Step1: Calculate books in full boxes

There are 8 full boxes, each with \( x \) books, so total from full boxes is \( 8x \).

Step2: Calculate books in half - full boxes

Each half - full box has \( \frac{1}{2}x \) books, and there are 4 half - full boxes. So total from half - full boxes is \( 4\times\frac{1}{2}x=2x \).

Step3: Add books not in boxes

There are 23 books not in any boxes. So the total number of books is the sum of books from full boxes, half - full boxes and the books not in boxes.
The equation is \( 8x + 2x+23=363 \), which simplifies to \( 10x + 23 = 363 \).

Answer:

\( 8x + 4\times\frac{1}{2}x+23 \) (or simplified as \( 10x + 23 \))