Final answer:
Alexis can have internet for a maximum of 16 months without spending more than $500.
Step-by-step explanation:
To find out how many months Alexis can have internet without spending more than $500, we need to consider the monthly cost of internet and the one-time connection fee. The monthly cost is $25 and the one-time fee is $99. Let's assume she can have internet for x months. Therefore, the total cost of internet will be $25x + $99, and this should not exceed $500. We can write this as an inequality:
25x + 99 ≤ 500
To solve for x, we need to isolate it on one side of the inequality. We can start by subtracting 99 from both sides:
25x ≤ 401
Next, we divide both sides by 25:
x ≤ 16.04
Since x represents the number of months, Alexis cannot have a fraction of a month. Therefore, she can have internet for a maximum of 16 months without spending more than $500.