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

Let's break this down step by step.

1. Weight of the container: Jerrica puts a container in the box that weighs 26 pounds.

2. Total weight capacity of the box: The box can hold at most 65 pounds.

3. Weight of each book: Each book weighs 1.3 pounds.

Now we want to represent the total weight of the container and the books in the box as an inequality.

Let \( x \) be the number of books Jerrica can put in the box. The total weight in the box can be expressed as:

\[ \text{Weight of container} + \text{Weight of books} \leq \text{Maximum weight capacity} \]

This means:

\[ 26 + 1.3x \leq 65 \]

Now, we can rearrange this inequality to solve for \( x \):

1. Subtract 26 from both sides:

\[ 1.3x \leq 65 - 26 \]

\[ 1.3x \leq 39 \]

2. Divide both sides by 1.3:

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

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

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

So, we can write the inequality as:

\[ x \leq 30 \]

Final answer

The inequality is:

\[ x + 26 \leq 65 \]

Jerrica can put at most 30 books in the box.

Summary

• Inequality: \( x + 26 \leq 65 \)
• Maximum number of books: 30 books.