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

__x+__ ≤__, where x is the number of books Jerrica can put in the box. Jerrica can put at most __ books in the box.

Answer 1

To find the inequality for the number of books Jerrica can put in the box, we start with the weight limit of the box and the current weight of the container she's already put inside.

The box can hold a maximum of 65 pounds, and Jerrica has already placed a container that weighs 26 pounds in the box.

Let \( x \) represent the number of books Jerrica can add. Each book weighs 1.3 pounds. Therefore, the total weight of the books will be \( 1.3x \) pounds.

The inequality representing the total weight in the box is: \[ 26 + 1.3x \leq 65 \]

To isolate \( x \), we'll first subtract 26 from both sides of the inequality: \[ 1.3x \leq 65 - 26 \] \[ 1.3x \leq 39 \]

Next, we'll divide both sides by 1.3: \[ x \leq \frac{39}{1.3} \] \[ x \leq 30 \]

Thus, the inequality can be rewritten as: \[ x \leq 30 \]

In summary:

1. The inequality for the number of books Jerrica can put in the box is \( x \leq 30 \).
2. Jerrica can put at most 30 books in the box.