Jerrica is packing a box that can hold at most 65 pounds. She starts by putting a container in the box that weighs 26 pounds. She plans to fill the rest of the box with books. Each book she places in the box weighs 1.3 pounds. Write an inequality for the number of books Jerrica can put in the box, and describe the solutions.(2 points)

Question

Jerrica is packing a box that can hold at most 65 pounds. She starts by putting a container in the box that weighs 26 pounds. She plans to fill the rest of the box with books. Each book she places in the box weighs 1.3 pounds. Write an inequality for the number of books Jerrica can put in the box, and describe the solutions.(2 points)
blank x+ 26 ≤ 65, where x
 is the number of books Jerrica can put in the box. Jerrica can put at most  
 books in the box.

GPT-4o mini · Accepted Answer

To formulate the inequality regarding the number of books Jerrica can put in the box, we start with the information provided:

The maximum weight the box can hold is 65 pounds.
The weight of the container already in the box is 26 pounds.
Each book weighs 1.3 pounds.

Let \( x \) represent the number of books Jerrica can add to the box. The total weight of the container and the books can be expressed as:

\[ 26 + 1.3x \]

Since this total weight cannot exceed 65 pounds, we write the inequality:

\[ 26 + 1.3x \leq 65 \]

To solve for \( x \), we first subtract 26 from both sides:

\[ 1.3x \leq 39 \]

Next, we divide both sides by 1.3:

\[ x \leq \frac{39}{1.3} \]

Calculating \( \frac{39}{1.3} \):

\[ \frac{39}{1.3} = 30 \]

Thus, we have the inequality:

\[ x \leq 30 \]

Summary of the Solution:

Jerrica can put at most 30 books in the box. The solutions to the inequality represent all the possible whole numbers of books \( x \) that Jerrica can place in the box, which are \( 0, 1, 2, \ldots, 30 \).