Question

Lucy is deciding between two different movie streaming sites to subscribe to. Plan A costs $8 per month plus $2.50 per movie watched. Plan B costs $20 per month plus $1.50 per movie watched. Let AA represent the monthly cost of Plan A if Lucy watches xx per month, and let BB represent the monthly cost of Plan B if Lucy watches xx movies per month. Write an equation for each situation, in terms of x, commax, and determine the interval of movies watched, x, commax, for which Plan A is cheaper than Plan B.

Answer 1

Step-by-step explanation:To determine the interval of movies watched for which Plan A is cheaper than Plan B, let's first write equations for each situation.

For Plan A, the monthly cost can be represented by AA. We know that Plan A costs $8 per month plus $2.50 per movie watched. So, the equation for Plan A is:

AA = 8 + 2.50x

where x represents the number of movies watched per month.

For Plan B, the monthly cost can be represented by BB. We know that Plan B costs $20 per month plus $1.50 per movie watched. So, the equation for Plan B is:

BB = 20 + 1.50x

Now, we need to find the interval of movies watched, x, for which Plan A is cheaper than Plan B.

To do this, we need to compare the costs of Plan A and Plan B. We can set up an inequality to represent this comparison:

AA < BB

Substituting the equations for AA and BB, we have:

8 + 2.50x < 20 + 1.50x

Simplifying the inequality, we get:

2.50x - 1.50x < 20 - 8

1x < 12

x < 12

Therefore, the interval of movies watched, x, for which Plan A is cheaper than Plan B is x < 12.

In other words, if Lucy watches fewer than 12 movies per month, Plan A will be cheaper for her compared to Plan B. If she watches 12 or more movies per month, Plan B will be cheaper.