1. **State the problem:** We have two taxi services with different pricing schemes: - Tim's Taxi charges a base fare of 5 plus 1.25 per mile. - Tara's Taxi charges a base fare of 4 plus 1.35 per mile. We want to find when the cost of both taxis is the same. 2. **Write the equations:** Tim's cost: $y = 5 + 1.25x$ Tara's cost: $y = 4 + 1.35x$ where $x$ is the number of miles. 3. **Set the costs equal to find when they are the same:** $$5 + 1.25x = 4 + 1.35x$$ 4. **Solve for $x$:** Subtract 4 from both sides: $$5 + 1.25x - 4 = 4 + 1.35x - 4$$ $$1 + 1.25x = 1.35x$$ Subtract $1.25x$ from both sides: $$1 + \cancel{1.25x} - \cancel{1.25x} = 1.35x - 1.25x$$ $$1 = 0.10x$$ Divide both sides by 0.10: $$\frac{1}{\cancel{0.10}} = \frac{0.10x}{\cancel{0.10}}$$ $$10 = x$$ 5. **Interpretation:** The cost is the same when the taxi ride is 10 miles. 6. **Calculate the cost at 10 miles:** Tim's cost: $$y = 5 + 1.25 \times 10 = 5 + 12.5 = 17.5$$ Tara's cost: $$y = 4 + 1.35 \times 10 = 4 + 13.5 = 17.5$$ Both cost 17.5 at 10 miles. **Final answer:** The cost is the same at 10 miles, and the cost is 17.5.