Taxi A charges $0.50 per mile and an initial fee of $3. Taxi B charges $0.75 per mile and an initial fee of $2. Which inequality represents the situation where the cost of Taxi B will be greater than Taxi A, where m is miles?

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.

Discover how to solve an inequality comparing the costs of Taxi A and Taxi B. Taxi A charges $0.50 per mile with a $3 initial fee, and Taxi B charges $0.75 per mile with a $2 initial fee. Learn the step-by-step solution to find when Taxi B is more expensive, suitable for Grades 7-9.

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