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You decide to rent a cottage you own. You spend $400 getting the cottage ready to put on the rental market. Your costs for utilities run approximately $15 per day. You think you can charge $115 per night in rent. Part A: Write an equation that represents your costs, C, in dollars for x number of nights. Part B: Write and equation that represents the Revenue (income), R, in dollars for x number of nights. Part C: What is the solution to this system of equations? Interpret the meaning of the solution.

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Answer:

Part A

The costs consist of one off payment to get the cottage ready and daily utility charges:

  • C = 400 + 15x

Part B

The revenue is the sum of daily rental:

  • R = 115x

Part C

To solve it as a system we make C= R or:

  • 400 + 15x = 115x

Solving we get:

  • 400 = 115x - 15x
  • 400 = 100x
  • x = 400/100
  • x = 4

It gives us:

  • C = 400 + 15*4 = 460
  • R = 115*4 = 460

The meaning of the solution is the number of nights we can pay off the costs and after 4 days we start to get profit.

Answer:

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