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Test
Math
Domain
Algebra
Skill
Linear inequalities in one or two variables
Difficulty
Medium
ID: 90bd9ef8
Modded SAT Question Bank by Abdullah Mallik

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?

  1. 25,000 is greater than, open parenthesis, 4,334 minus 2,712, close parenthesis, times t
  2. 25,000 is less than, open parenthesis, 4,334 minus 2,712, close parenthesis, times t
  3. 25,000 minus 4,334, is greater than 2,712 t
  4. 25,000 is greater than the fraction with numerator 4,332, and denominator 2,712, end fraction, t
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Correct Answer: B
Rationale

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 minus 2,712 dollars. In t years, the savings will be open parenthesis, 4,334 minus 2,712, close parenthesis, times 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 is less than, open parenthesis, 4,334 minus 2,712, close parenthesis, times t.

Choice A is incorrect. It gives the number of years after installation at which the total amount of energy cost savings will be less than the installation cost. Choice C is incorrect and may result from subtracting the average annual energy cost for the home from the onetime cost
of the geothermal heating system installation. To find the predicted total savings, the predicted average cost should be subtracted from the average annual energy cost before the installation, and the result should be multiplied by the number of years, t. Choice D is incorrect and may result from misunderstanding the context. The ratio 4,332 over 2,712 compares the average energy cost before installation and the average energy cost after installation; it does not represent the savings.

Question Difficulty: Medium
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