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As the number of pages in a photo book increases, the price of the book also increases. There is an additional shipping charge of 15%. The price of a book can be modeled by the equation below, where P = the price of the book, 20 is the printing charge, 0.5 is the charge per page, and x = the number of pages:

P = (20 + 0.5x) + 0.15(20 + 0.5x)

Jennifer wants to purchase a book but only has $62.10 to spend. What is the maximum number of pages she can have in her book?

Will give Hand Jobliest!!!

Respuesta :

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Everything's already there, you just to identify the value for P.
Since $62.10 is the maximum budget Jennifer can spend, we can conclude that this is also the maximum price of the book. (P = $62.10) 

To get the number of pages she can have, simply substitute the value of P in the equation such that: 
P = (20 + 0.5x) + 0.15(20 + 0.5x) 
$62.10 = (20 + 0.5x) + 0.15(20 + 0.5x) 

With the formula above, you can now solve for x 

62.10 = 20 + 0.5x + 0.15(20) + 0.15(0.5x) 
62.10 = 20 + 0.5x + 3 + 0.075x 
62.10 = (0.5x + 0.075x) + (20 + 3) 
62.10 = 0.575x + 23 
62.10 - 23 = 0.575x + 23 - 23 
39.10 = 0.575x (divide both sides by 0.575) 
x = 68 pages

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