Question

Luis is deciding between two different movie streaming sites to subscribe to. Plan A costs $20 per month plus $1 per movie watched. Plan B costs $12 per month plus $3 per movie watched. Let AA represent the monthly cost of Plan A if Luis watches xx per month, and let BB represent the monthly cost of Plan B if Luis watches xx movies per month. Graph each function and determine the interval of movies watched, x, commax, for which Plan A is cheaper than Plan B.

Answer 1

To find the costs for both plans based on the number of movies watched \( x \), we can define the monthly cost functions for both plans:

1. Plan A: \[ A(x) = 20 + 1x = 20 + x \]

2. Plan B: \[ B(x) = 12 + 3x \]

Next, we will graph these two functions and determine the intervals where Plan A is cheaper than Plan B. To find this interval, we need to solve the inequality:

\[ A(x) < B(x) \]

Substituting in the functions we derived earlier:

\[ 20 + x < 12 + 3x \]

Now, we will solve for \( x \):

1. Subtract \( x \) from both sides:

\[ 20 < 12 + 2x \]

2. Subtract 12 from both sides:

\[ 8 < 2x \]

3. Divide by 2:

\[ 4 < x \] or \[ x > 4 \]

This means that Plan A is cheaper than Plan B when Luis watches more than 4 movies per month.

Summary:

• Plan A is cheaper than Plan B for \( x > 4 \).

• To visualize this, you can graph both linear functions on the same coordinate system:

• Plan A (linear line starting at (0, 20) with a slope of 1).

• Plan B (linear line starting at (0, 12) with a slope of 3).

Where the line representing Plan A is below the line for Plan B indicates the intervals of \( x \) values where Plan A is cheaper. The point at which they intersect occurs when \( x = 4 \).

Intervals:

• Plan A is cheaper when \( x > 4 \) (Luis watches more than 4 movies per month).