Question

Mike's Video store charges 5.00 to rent a video game with no monthly fee, Club Video charges only 3.50 to rent a game plus a yearly fee of 50.00. The yearly cost to rent videos games depends on the number of video games, x, rented. Write an inequality that represents the situation when the yearly cost of Club Video store is less than the yearly cost of Mike's Video?

Answer 1

To find when Club Video is less expensive annually than Mike's Video, the inequality $3.50x + $50.00 < $5.00x is used, signifying that the yearly cost to rent games from Club Video, including their yearly fee, is less than the cost from Mike's Video as long as the inequality holds true for the number of games rented.

Step-by-step explanation:

When comparing the yearly cost of renting video games from Mike's Video and Club Video, we define two equations to represent the cost from each store:

• Mike's Video: Total cost with no monthly fee = $5.00 × number of games rented (x)
• Club Video: Total cost with a yearly fee = $3.50 × number of games rented (x) + $50.00 yearly fee

To determine when Club Video is less expensive than Mike's Video over the course of a year, we set up the following inequality:

$3.50x + $50.00 < $5.00x

This inequality shows that Club Video's annual cost including the yearly fee will be less than the cost of renting the same number of games from Mike's Video when the inequality is true.