18. Which of the following situations best represents the inequality 0.60x + 150 < 200?
A: A car towing service charges $150 to pick up the car and then $0.60 per mile to tow it. What is the greatest number of miles a car can be towed for less than $200?
B: Genny transcribes audio files for $0.60 per minute, plus a $150 flat fee. After how many minutes will Genny's fee be more than $200?
C: Both A and B
A
The situation that best represents the inequality 0.60x + 150 < 200 is option A.
In option A, a car towing service charges $150 as a flat fee to pick up the car, and then $0.60 per mile to tow it. The question asks for the greatest number of miles a car can be towed for less than $200.
To find the answer, we can set up the inequality: 0.60x + 150 < 200, where x represents the number of miles.
Subtracting 150 from both sides of the inequality gives us: 0.60x < 50.
To isolate the variable, we divide both sides of the inequality by 0.60: x < 50 / 0.60.
Simplifying the right side gives us: x < 83.33.
Therefore, the car can be towed for less than $200 for a maximum of 83.33 miles.
To determine which situation best represents the inequality 0.60x + 150 < 200, we can analyze each option.
Option A describes a car towing service that charges $150 to pick up the car and $0.60 per mile to tow it. The question asks for the greatest number of miles a car can be towed for less than $200. This aligns with the given inequality 0.60x + 150 < 200, where x represents the number of miles.
Option B presents a scenario where Genny transcribes audio files for $0.60 per minute, along with a $150 flat fee. The question asks for how many minutes Genny's fee will exceed $200. Although this situation involves a similar structure, it does not correspond to the given inequality.
Considering this, we can conclude that Option A correctly represents the inequality 0.60x + 150 < 200. Therefore, the best answer is A.