To determine the inequality for the number of books Jerrica can put in the box, we first recognize the constraints provided by the box's maximum weight capacity and the weight of the container already placed in the box.
- The maximum weight capacity of the box is 65 pounds.
- The weight of the container already in the box is 26 pounds.
- Each book weighs 1.3 pounds.
Since Jerrica already has 26 pounds in the box, we can define the weight of the books she plans to add:
- Let \( x \) be the number of books.
- The total weight of the books will be \( 1.3x \) pounds.
The total weight in the box (the container plus the books) must be less than or equal to 65 pounds. Therefore, we can set up the following inequality:
\[ 26 + 1.3x \leq 65 \]
Now, we can isolate \( x \) in this inequality to find out how many books can be added:
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Subtract 26 from both sides: \[ 1.3x \leq 65 - 26 \] \[ 1.3x \leq 39 \]
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Divide both sides by 1.3 to solve for \( x \): \[ x \leq \frac{39}{1.3} \] \[ x \leq 30 \]
Thus, we have the complete inequality: \[ x \leq 30 \]
Solution Description:
- \( x \) represents the number of books Jerrica can add to the box. The solutions to the inequality \( x \leq 30 \) are all the non-negative integers (whole numbers) that satisfy the condition, meaning Jerrica can put anywhere from 0 books up to a maximum of 30 books in the box without exceeding the weight limit. Therefore, Jerrica can put at most 30 books in the box.