Question

Write a one-variable inequality to represent each problem.

1. Taxi A charges $0.60 per mile and an initial fee of $4. Taxi B charges $0.90 per mile and an initial fee of $3. When will the cost of Taxi B be greater than Taxi A, where m is miles?

2. Renting video games from Store A costs $4.50 per game plus a monthly fee of $8.50. Renting video games from Store B costs $6.00 per game with no monthly fee. The monthly cost to rent video games depends on the number of video games, v rented. When will the monthly cost at Store A be less than the monthly cost at Store B?

Answer 1

1. 0.90m + 3 > 0.60m + 4; 2. 4.50v + 8.50 < 6.00v

Explanation:

1. Taxis

Let A = cost of Taxi A

and B = cost of Taxi B

Then A = 0.60m + 4

and B = 0.90m +3

If B > A, then

0.90m + 3 > 0.60m + 4

2. Video games

Let A = monthly cost at Store A

and B = monthly cost at Store B

Then A = 4.50v + 8.50

and B = 6.00v

If A < B, then

4.50v + 8.50 < 6.00v