Final answer:
The greatest number of games Rosa can buy with her budget, according to the inequality 3.50⋅k + 5.00 ≤ 25.00, is 5 games.
Step-by-step explanation:
The inequality 3.50⋅k + 5.00 ≤ 25.00 represents the budget constraint Rosa faces when purchasing games. To find the greatest number of games, k, she can buy, we first isolate k by subtracting 5.00 from both sides of the inequality:
3.50⋅k ≤ 25.00 - 5.00
3.50⋅k ≤ 20.00
Now, we divide both sides by 3.50 to solve for k:
k ≤ 20.00 / 3.50
k ≤ 5.71
Since Rosa can only buy a whole number of games, and k must be less than or equal to 5.71, the greatest number of games she can buy is 5 games.