Final answer:
The inequality to represent Vanessa's spending on travel and lodging being less than her budget is x + ny < z, where x is the total cost for plane tickets, y is the cost per night at the hotel for n nights, and z is the total budget.
Step-by-step explanation:
The question posed is regarding how to represent Vanessa's travel and lodging budget situation with an inequality. She has budgeted a certain amount for her vacation, found round trip plane tickets for a certain total dollar amount represented by x, and a hotel that charges a dollar amount per night represented by y.
Vanessa plans to stay in the hotel for a number of nights represented by n, and the inequality should reflect that she spends less than her budgeted amount, which we'll call z. If she spends x dollars on plane tickets and ny dollars on the hotel stay, the total spending on travel and lodging will be x + ny.
To say that Vanessa spends less than her budgeted amount, we would use the inequality x + ny < z. This inequality correctly shows that the sum of her expenses for plane tickets and the hotel should be less than her total budget for travel and lodging. Therefore, the correct inequality that best describes the scenario is option 1) x + y < z.