Final answer:
The inequality representing the budget problem for purchasing desks and a vending machine is 15d + $450 ≤ $1600. This reflects the cost of the desks multiplied by the number of desks (d) plus the cost of the vending machine, which should not exceed the school's budget.
Step-by-step explanation:
The Southside school has a total budget of $1600 to spend on desks and a vending machine. If each desk costs $15 and the vending machine costs $450, we can represent the inequality for the number of de (sksd) that can be purchased with the remaining budget as:
15d + $450 ≤ $1600
This inequality shows that the cost of desks multiplied by the number of desks (d) plus the cost of the vending machine should be less than or equal to the total budget available. Solving for d gives us the maximum number of desks the school can purchase.