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The amount of revenue in dollars, y, that Makayla receives from selling x posters is given by the equation y = 3x. The cost of producing x posters is given by the equation y = LaTeX: \frac{1}{3}x\:+\:2001 3 x + 200. How many posters does Makayla need to sell so that the cost and revenue are equal?
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Respuesta :

MrRoyal

Answer:

75 posters

Step-by-step explanation:

Given

[tex]y = 3x[/tex] ----  Revenue

[tex]y = \frac{x}{3} + 200[/tex] --Cost of production

Required

Determine the number of posters that when cost equals revenue

To do this, we simply equate both equations

i.e. [tex]3x = \frac{x}{3} + 200[/tex]

Collect like terms.

[tex]3x - \frac{x}{3} = 200[/tex]

Multiply through by 3

[tex]3(3x - \frac{x}{3}) = 200*3[/tex]

[tex]9x - x = 600[/tex]

[tex]8x = 600[/tex]

Divide both sides by 8

[tex]\frac{8x}{8} = \frac{600}{8}[/tex]

[tex]x = \frac{600}{8}[/tex]

[tex]x = 75[/tex]

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