Final answer:
Ben can buy a maximum of 18 packages of pretzels after purchasing a notebook and setting aside money for savings. The correct inequality is 0.5x + 7.25 + 2.75 ≤ 19 and after solving it, x ≤ 18 represents the maximum number of pretzel packages he can purchase.
Step-by-step explanation:
We need to find the inequality that represents the maximum number of packages of pretzels Ben can buy with his remaining money after buying a notebook and saving $2.75. First, let's calculate Ben's remaining money after purchasing the notebook and setting aside the savings.
Ben has $19 to start with and spends $7.25 on the notebook and needs to save $2.75, which leaves him with
$19 - $7.25 - $2.75 = $9.00.
Now, if pretzels cost $0.50 per package, we want to find out how many packages 'x' Ben can buy without spending more than his remaining $9.00.
The correct inequality to represent this scenario is
0.5x + 7.25 + 2.75 ≤ 19.
This inequality states that the cost of 'x' number of pretzel packages at $0.50 each, plus the cost of the notebook and the amount Ben wants to save, should not exceed $19. Now, let's solve it:
0.5x + 7.25 + 2.75 ≤ 19
0.5x + 10 ≤ 19
0.5x ≤ 9
x ≤ 18
Therefore, Ben can buy a maximum of 18 packages of pretzels.