The cost of each taxi can be represented by an equation, where $m$ is the number of miles traveled.

• For Taxi A: $C_A = 0.50m + 3$
• For Taxi B: $C_B = 0.75m + 2$

To find when the cost of Taxi B is greater than Taxi A, we need to set up the inequality: $C_B > C_A$ Substitute the expressions for $C_B$ and $C_A$: $0.75m + 2 > 0.50m + 3$

Now solve the inequality step by step:

1. Subtract $0.50m$ from both sides: $0.25m + 2 > 3$

2. Subtract 2 from both sides: $0.25m > 1$

3. Divide both sides by 0.25: $m > 4$

Thus, the inequality that represents when Taxi B will be more expensive than Taxi A is: $m > 4$

This means Taxi B will cost more than Taxi A when the distance traveled is greater than 4 miles.

Would you like more details, or do you have any questions?

Here are 5 related questions to explore:

1. How would the inequality change if the initial fee for Taxi B increased to $4?
2. What is the cost comparison at exactly 4 miles? Are the costs the same?
3. If you only traveled 2 miles, which taxi would be cheaper?
4. How does the cost for Taxi A increase as the number of miles traveled increases?
5. What if Taxi A changed its rate to $0.60 per mile but kept the same initial fee?

Tip: Always set up equations or inequalities based on the situation’s conditions, and then solve step by step.