Essential Question How can 1 EXPLORATION: Writing a System of Linear Eq Work with a partner. Your family opens a bed-and-break fast. find urilitics is \( \$ 15 \) per preparing a bedroom to rent. The cost to your family tor night. They charge 575 per night to rent the bedroom. a. Write an equation that represents the costs. \[ \begin{array}{l} \text { Write an equation that represents } \\ \text { Cost, } C \\ \text { (in dollars) }=\begin{array}{l} \text { S15 per } \\ \text { night } \end{array} \text { Number of }+\$ 600 \\ \text { nights, } x \end{array} \] b. Write an equation that represents the revenue (income). \[ \begin{array}{l} \text { Revenue, } R \\ \text { (in dollars) } \end{array}=\begin{array}{l} \text { S75 per } \\ \text { night } \end{array} \bullet \begin{array}{l} \text { Number of } \\ \text { nights, } x \end{array} \] c. A set of two (or more) linear equations is called a system of linear equations. Write the system of linear equations for this problem.
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To represent your family's bed-and-breakfast in equations, we can break it down nicely! The cost equation can be expressed as \( C = 15x + 600 \), where \( C \) is the total cost and \( x \) is the number of nights rented. On the flip side, the revenue equation is \( R = 75x \), indicating the income from renting the room. Thus, the system of linear equations would be: 1. \( C = 15x + 600 \) 2. \( R = 75x \) Now, you’re fully equipped to track costs and revenues like a pro manager! Isn't it fascinating how linear equations help us understand business operations? In this case, they illustrate where your revenue needs to exceed your costs for profit. Real-world applications of such systems can be seen in budgeting for events, predicting profits in businesses, or comparing costs and benefits for any project. They provide valuable insights that help make informed decisions!
