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: (2 points)

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?

x =
pages

Question

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: (2 points)

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?

x = 
 pages

supie · Answer

Solving for P

Given:
$$P = (20 + 0.5x) + 0.15(20 + 0.5x)$$$$P = $ 62.10$$ So every P turns into 62.10 $$$62.10 = (20 + 0.5x) + 0.15(20 + 0.5x) $$Solving for x$$62.10 = 20 + 0.5x + 0.15(20) + 0.15(0.5x) $$$$62.10 = 20 + 0.5x + 3 + 0.075x$$ Combining like terms$$62.10 = (0.5x + 0.075x) + (20 + 3) $$$$62.10 = 0.575x + 23$$ -23 from both sides $$39.10 = 0.575x$$ (divide both sides by 0.575)  $$so\ x = 68$$