The operating costs for a local business per year are a...

The operating costs for a local business per year are a fixed amount of $\$ 15,000$ and $\$ 2,500$ per day. a. Find $C$ that represents operating costs for the company, which depend on the number of days open, $x$. b. If the business accrues $\$ 5,515,000$ in annual operating costs, how many days did the business operate during the year?

The operating costs for a local business per year are a fixed amount of $\$ 15,000$ and $\$ 2,500$ per day.
a. Find $C$ that represents operating costs for the company, which depend on the number of days open, $x$.
b. If the business accrues $\$ 5,515,000$ in annual operating costs, how many days did the business operate during the year?

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Key Concepts

Linear Function Modeling

This concept involves representing real-world situations with linear functions, where the relationship between variables is expressed in the form y = mx + b. In this case, the operating cost is modeled as a combination of a fixed cost (the y-intercept) and a variable cost multiplied by the number of days open (the slope).

Fixed and Variable Costs

Fixed costs are expenses that do not change with the level of activity; they remain constant regardless of how many days the business operates. Variable costs, on the other hand, change in direct proportion to the activity level, such as the cost incurred per day of operation. Understanding both types is crucial in formulating a comprehensive cost model.

Solving Linear Equations

Once the linear function is established, solving for an unknown variable involves isolating that variable using algebraic operations. This technique is applied when setting the cost function equal to a known total cost and then solving for the number of days, demonstrating how mathematical equations can be used to derive practical business insights.

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