Set 5: Linear Equations (Advanced)

Choice D is correct. Choice C is the correct answer. We model this with $0.50x + 30 = 55$, where $x$ is miles. 1. Set up equation: $0.50x + 30 = 55$ 2. Subtract 30 from both sides: $0.50x = 55 - 30$ 3. Simplify: $0.50x = 25$ 4. Divide both sides by 0.50: $x = \frac{25}{0.50}$ 5. Simplify: $x = 50$ 6. Verify: $0.50(50) + 30 = 25 + 30 = 55$ ✓ So, you drove 50 miles. Choice C is incorrect because this results from adding 30 to 55: $85$, then dividing by 0.50: $170$. You subtract the daily rate. Choice D is incorrect because this is the cost of the mileage ($25), not the number of miles. Choice B is incorrect because this results from multiplying 25 by 0.50: 12.$5$. You need to divide.