SAT question 90bd9ef8 (Linear Inequalities)

Question

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?

38

Difficulty:Medium

A

$25, 000 > (4, 334 - 2, 712) t$

B

$25, 000 < (4, 334 - 2, 712) t$

C

$25, 000 - 4, 334 > 2, 712 t$

D

$25, 000 > \frac{4 , 334}{2 , 712} t$

College Board · Accepted Answer

The correct answer is B. 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 . 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 .

CookSAT · Answer

Note: The yearly savings are 4334-2712, so after t years they must exceed 25000.

Explanation

Enter in Desmos:

Why the other choices are wrong

SAT Question 90bd9ef8: Linear Inequalities answer and explanation with Desmos solution

Explanation

Enter in Desmos:

Why the other choices are wrong