You are planning a trip to Las Vegas and want to calculate...

You are planning a trip to Las Vegas and want to calculate your expected costs for the trip. You found that you can take a tour bus trip for up to 7 days, and it will cost you $\$ 225$ for the round trip. You figure that you can stay at a hotel and eat for about $\$ 150$ per day. a. Write an equation for the total cost of this trip depending on the number of days you stay. (We will ignore the gambling budget.) b. How much will it cost for a 3 -day trip? c. If you have $\$ 1200$ and want to gamble half of it, how many days can you stay in Las Vegas, assuming that you do not win any money?

You are planning a trip to Las Vegas and want to calculate your expected costs for the trip. You found that you can take a tour bus trip for up to 7 days, and it will cost you $\$ 225$ for the round trip. You figure that you can stay at a hotel and eat for about $\$ 150$ per day.
a. Write an equation for the total cost of this trip depending on the number of days you stay. (We will ignore the gambling budget.)
b. How much will it cost for a 3 -day trip?
c. If you have $\$ 1200$ and want to gamble half of it, how many days can you stay in Las Vegas, assuming that you do not win any money?

Key Concepts

Linear Inequalities

Linear inequalities are used when relationships between variables involve ranges rather than specific values. In budgeting problems, they help determine how many days one can afford to stay within a particular budget. By setting up an inequality with the total cost expression and the available funds, one can solve for the maximum number of days allowed.

Substitution

Substitution is the method of replacing a variable with a given numeric value to compute a specific result. When calculating the cost for a 3-day trip, the variable representing the number of days is substituted with 3 in the established linear equation, allowing for an exact numerical evaluation.

Budgeting Methods

Budgeting methods involve planning and allocating resources to ensure expenditures do not exceed available funds. Algebraic techniques like forming equations and solving inequalities aid in making informed decisions about spending, such as determining the feasible number of days for a trip based on fixed and variable costs.

Linear Functions

Linear functions are mathematical expressions that depict a straight-line relationship between two variables, usually in the form y = mx + b. In the context of cost calculations, the total cost is expressed as a fixed amount plus an additional amount that increases linearly with the number of days spent, illustrating a direct proportionality between the days and the variable cost.

Fixed and Variable Costs

Fixed costs remain constant regardless of the number of days, while variable costs change with usage or duration. In the problem, the tour bus ticket is a fixed cost, and the daily expenses for the hotel and meals represent the variable cost. Understanding this distinction is key in setting up an equation to model total costs.

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