1. **Problem statement:** A taxi company charges an initial fee of 8 plus 1.50 per mile. We need to write an equation for the total cost $y$ of riding $x$ miles, find the cost for 20 miles, and find the miles traveled if the cost is 29. 2. **Write the equation:** The total cost $y$ is the sum of the initial fee and the cost per mile times the number of miles. This gives: $$y = 8 + 1.50x$$ 3. **Calculate cost for 20 miles:** Substitute $x=20$ into the equation: $$y = 8 + 1.50 \times 20$$ $$y = 8 + 30 = 38$$ So, the cost for 20 miles is 38. 4. **Find miles for cost 29:** Set $y=29$ and solve for $x$: $$29 = 8 + 1.50x$$ Subtract 8 from both sides: $$29 - 8 = 1.50x$$ $$21 = 1.50x$$ Divide both sides by 1.50: $$\frac{21}{\cancel{1.50}} = \cancel{1.50}x \Rightarrow x = 14$$ So, the taxi traveled 14 miles when the cost was 29.