Final answer:
After spending $7.25 on a notebook, Ben has $11.75 left. Each package costs $0.50, and Ben can purchase a maximum of 23 packages with his remaining money. The inequality representing this scenario is n ≤ 23, where n is the number of packages.
Step-by-step explanation:
To find the inequality representing the maximum number of packages Ben can buy with his remaining money, we need to consider the initial amount he has, the cost of the notebook he bought, and the price per package. Ben started with $19 and spent $7.25 on a notebook. Now, we need to subtract the cost of the notebook from the initial amount to find out how much money Ben has left:
Total money left = Initial money - Cost of the notebook
Total money left = $19 - $7.25 = $11.75
Each package costs $0.50, so to find the maximum number of packages (n) Ben can buy, we set up the following inequality:Cost per package × n ≤ Total money left
$0.50 × n ≤ $11.75
To solve for n, divide both sides by the cost per package:
n ≤ $11.75 / $0.50
n ≤ 23.5
Since Ben cannot buy half a package, we need to consider only whole numbers. Therefore, the maximum number of packages Ben can buy is 23.The inequality representing the maximum number of packages Ben can afford is:
n ≤ 23