Question

colton is deciding between two different movie streaming sites to subscribe to. plan a costs $9 per month plus $2.50 per movie watched. let a represent the monthly cost of plan a if colton watches x per month, and let b represent the monthly cost of plan b if colton watches x movies per month. write an equation for each situation, in terms of x, and determine the interval of movies watched, x, for which plan a is cheaper than plan b.
answer
attempt 1 out of 2
a =

b =

plan a is cheaper than plan b when x

.

Explanation:

Step1: Define Cost for Plan A

Plan A has a fixed cost of $9 per month and $2.50 per movie. So the cost function \( A = 9 + 2.50x \).

Step2: Define Cost for Plan B

Plan B has a fixed cost of $21 per month and $1.50 per movie. So the cost function \( B = 21 + 1.50x \).

Step3: Find When A < B

Set up the inequality \( 9 + 2.50x < 21 + 1.50x \). Subtract \( 1.50x \) from both sides: \( 9 + x < 21 \). Subtract 9 from both sides: \( x < 12 \).

Answer:

\( A = 9 + 2.5x \)
\( B = 21 + 1.5x \)
Plan A is cheaper than Plan B when \( x < 12 \) (for valid \( x \) in domain).