Question

Easton is deciding between two different movie streaming sites to subscribe to. Plan A costs $16 per month plus $2 per movie watched. Plan B costs $20 per month plus $1 per movie watched. Let A represent the monthly cost of Plan A if Easton watches x per month, and let B represent the monthly cost of Plan B if Easton watches x movies per month. Graph each function and determine the interval of movies watched, x, for which Plan A is cheaper than Plan B.

Answer 1

a) The graph of each function for Plan A and Plan B is as follows:

| A

|

| /

| /

| /

| /

|/

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x | B

b) The interval of movies watched, x, for which Plan A is cheaper than Plan B is x < 4.

Plan A Plan B

Fixed monthly cost $16 $20

Variable cost per movie $2 $1

Let the monthly cost of Plan A = A

Let the monthly cost of Plan B = B

Let the number of movies watched by Easton per month = x

A = 16 + 2x

B = 20 + x

Graphing these functions:

The x-axis represents the number of movies watched per month, and the y-axis represents the monthly cost.

The graph of A(x) is a line with a slope of 2 and a y-intercept of 16. The graph of B(x) is a line with a slope of 1 and a y-intercept of 20.

For the monthly cost of Plan A and Plan B to be equal:

16 + 2x = 20 + x

x = 4

When x < 4, Plan A will be cheaper than Plan B.

Check (x = 3)

A = 16 + 2(3) = $22

B = 20 + 3 = $23