Answered

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PLZ HELP ILL GOVE YOU BRAINLIEST
Damian is deciding between two different movie streaming sites to subscribe to. Plan
A costs $33 per month plus $3 per movie watched. Plan B costs $37 per month plus
$2 per movie watched. Let A represent the monthly cost of Plan A if Damian watches
x per month, and let B represent the monthly cost of Plan B if Damian watches x
movies per month. Write an equation for each situation, in terms of x, and determine
the number of monthly movies watched, x, that would make the two plans have an
equal monthly cost.

Sagot :

Using linear functions, it is found that:

  • The equation for Plan A is: [tex]C_a(x) = 33 + 3x[/tex]
  • The equation for Plan B is: [tex]C_b(x) = 37 + 2x[/tex]
  • The monthly plans would have an equal cost when 4 movies are watched.

A linear function for a cost depending on the number of movies x is given by:

[tex]C(x) = C(0) + ax[/tex]

In which:

  • C(0) is the fixed cost.
  • a is the cost per movie.

For Plan A, $33 per month plus $3 per movie watched, hence [tex]C(0) = 33, a = 3[/tex], and the equation is:

[tex]C_a(x) = 33 + 3x[/tex]

For Plan B, $37 per month plus  $2 per movie watched, hence [tex]C(0) = 37, a = 2[/tex], and the equation is:

[tex]C_b(x) = 37 + 2x[/tex]

The monthly cost is equal when:

[tex]C_a(x) = C_b(x)[/tex]

[tex]33 + 3x = 37 + 2x[/tex]

[tex]x = 4[/tex]

The monthly plans would have an equal cost when 4 movies are watched.

A similar problem is given at https://brainly.com/question/16302622

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