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.

Answer 1

To write the inequality for the number of books Jerrica can put in the box, we start by considering the weight limit of the box and the weights of the items already in it.

1. The total weight that the box can hold is 65 pounds.
2. Jerrica has already placed a container that weighs 26 pounds in the box.
3. Each book weighs 1.3 pounds, and we will let \( x \) represent the number of books.

The total weight in the box can be expressed as the weight of the container plus the weight of the books, which gives us the following inequality:

\[ 26 + 1.3x \leq 65 \]

Next, we can simplify this inequality:

1. Subtract 26 from both sides: \[ 1.3x \leq 39 \]

2. Now, divide both sides by 1.3: \[ x \leq \frac{39}{1.3} \]

Calculating the division gives: \[ x \leq 30 \]

So, we can write the final inequality as: \[ x \leq 30 \]

Solutions:

The solution indicates that Jerrica can place up to 30 books in the box without exceeding the weight limit of 65 pounds. The possible values for \( x \) are all non-negative integers from 0 to 30, inclusive. Thus, \( x \) can be any whole number such that \( 0 \leq x \leq 30 \).