Final answer:
The maximum number of video games and movies that can be purchased within the given budget is 2 video games and 7 movies.
Step-by-step explanation:
To solve this problem, we can use algebraic equations. Let's assume the number of video games purchased is x and the number of movies purchased is y. We are given that video games cost $28 each and movies are $8 each. The total purchase was no more than $80.
We can use the equation 28x + 8y ≤ 80 to represent the total cost of the video games and movies. We need to find the maximum values of x and y that satisfy this equation.
By substituting different values of x and y, we can find the combination that gives us the greatest total number of video games and movies within the given budget. For example, when x = 2 and y = 7, the total cost is 28(2) + 8(7) = 56 + 56 = 112, which is greater than $80. However, when x = 3 and y = 8, the total cost is 28(3) + 8(8) = 84 + 64 = 148, which is greater than $80. Therefore, the maximum values of x and y that satisfy the equation are x = 2 and y = 7. This means that the student can purchase a maximum of 2 video games and 7 movies within the given budget.