Your family is planning a trip to Orlando, Florida, to visit...

Your family is planning a trip to Orlando, Florida, to visit the amusement parks. You want to budget for your expected costs. You find round trip flights for your four-person family that total $\$ 1600 .$ You expect the hotel, food, and admissions to cost about $\$ 900$ per day. a. Write an equation for the total cost of this trip depending on the number of days you stay. b. How much will it cost for a 5 -day trip? c. If your family can afford to spend $\$ 7500$ on this trip, how many days can you stay in Orlando?

Your family is planning a trip to Orlando, Florida, to visit the amusement parks. You want to budget for your expected costs. You find round trip flights for your four-person family that total $\$ 1600 .$ You expect the hotel, food, and admissions to cost about $\$ 900$ per day.
a. Write an equation for the total cost of this trip depending on the number of days you stay.
b. How much will it cost for a 5 -day trip?
c. If your family can afford to spend $\$ 7500$ on this trip, how many days can you stay in Orlando?

Key Concepts

Cost Modeling

Cost modeling involves creating an equation that represents the total cost as the sum of fixed and variable costs. In budgeting scenarios, this means accounting for expenses that remain constant regardless of usage (such as flights) and those that vary with the quantity (such as daily expenses). This approach is crucial for planning and making informed financial decisions.

Linear Functions

Linear functions describe relationships where one variable changes at a constant rate with respect to another. In cost modeling, a linear function can represent the total cost as a fixed cost plus a variable cost multiplied by the number of days. This type of function is fundamental in many real-world applications, including budgeting and forecasting expenses.

Substitution Method

The substitution method involves replacing variables in an equation with specific values to compute a result. In a cost equation, substituting the number of days into the linear function directly calculates the total cost for that duration, providing a straightforward way to evaluate scenarios or options.

Inequalities and Budget Constraints

Inequalities are used to express conditions where one quantity must be less than or equal to another, such as staying within a budget. By setting up an inequality with the cost function, one can determine the maximum number of days allowable given specific financial constraints. This technique is essential for ensuring that spending does not exceed available funds.

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