Explanation
Correct answer: D.
Choice D is correct. It’s given that Adam charges a fee of $ for his equipment and $ per hour spent working on the project. For hours spent working on the project, it follows that Adam's total charge, in dollars, is . It's also given that Caroline charges a fee of $ for her equipment and $ per hour spent working on the project. For hours spent working on the project, it follows that Caroline's total charge, in dollars, is . Therefore, if represents the number of hours spent working on the landscaping project, then Caroline's total charge is greater than Adam's total charge if , or . Subtracting from both sides of this inequality yields . Subtracting from both sides of this inequality yields . Dividing both sides of this inequality by yields .
Desmos solution:
Note: The boundary occurs at 6, and Caroline’s charge is greater above that point.
Enter in Desmos:
Reviewed and rewritten by CookSAT
Why the other choices are wrong
Choice A
Choice A is incorrect. For example, if , then Caroline’s total charge, in dollars, would be , or , and Adam’s total charge, in dollars, would be , or . Since Caroline’s total charge would be less than Adam’s total charge, can’t be a possible value of .
Choice B
Choice B is incorrect. For example, if , then Caroline’s total charge, in dollars, would be , or , and Adam’s total charge, in dollars, would be , or . Since Caroline’s total charge would be equal to Adam’s total charge, can’t be a possible value of .
Choice C
Choice C is incorrect. For example, if , then Caroline’s total charge, in dollars, would be , or , and Adam’s total charge, in dollars, would be , or . Since Caroline’s total charge would be less than Adam’s total charge, can’t be a possible value of .