The average annual energy cost for a certain home is $4,334. The homeowner plans to spend $25,000 to install a geothermal heating system. The homeowner estimates that the average annual energy cost will then be $2,712. Which of the following inequalities can be solved to find t, the number of years after installation at which the total amount of energy cost savings will exceed the installation cost?

Correct answer: B. 25,000 < (4,334 − 2,712)t

  • A. 25,000 > (4,334 − 2,712)t
  • B. 25,000 < (4,334 − 2,712)t
  • C. 25,000 − 4,334 > 2,712t
  • D. 25,000 > (4,332/2,712)t

Explanation

Choice B is correct. The savings each year from installing the geothermal heating system will be the average annual energy cost for the home before the geothermal heating system installation minus the average annual energy cost after the geothermal heating system installation, which is (4,334 − 2,712) dollars. In t years, the savings will be (4,334 − 2,712)t dollars. Therefore, the inequality that can be solved to find the number of years after installation at which the total amount of energy cost savings will exceed (be greater than) the installation cost, $25,000, is 25,000 < (4,334 − 2,712)t.

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