Set 1: Linear Equations (Advanced)

Choice C is correct. Choice C is the correct answer. We can model this with the equation $2x + 5 = 25$, where $x$ is the number of miles. 1. Set up equation: $2x + 5 = 25$ 2. Subtract 5 from both sides: $2x = 25 - 5$ 3. Simplify: $2x = 20$ 4. Divide both sides by 2: $x = \frac{20}{2}$ 5. Simplify: $x = 10$ 6. Verify: $2(10) + 5 = 20 + 5 = 25$ ✓ So, the ride was 10 miles long. Choice D is incorrect because this results from adding 5 to 25: $30$, then $30 /2 = 15$. You subtract the base fare, not add it. Choice C is incorrect because this is the cost of the miles ($20), not the number of miles. Choice A is incorrect because this results from dividing the total fare by the rate:$25 /2 = 12.5$. This ignores the base fare.