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?

Given:

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

$62.10 is the maximum budget Jennifer can spend.

So,

The maximum price a book can have would be $62.10

Substituting the value of P in the equation:

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

P = $ 62.10

Therefore,

$62.10 = (20 + 0.5x) + 0.15 (20 + 0.5x)

Now solving for x we get:

62.10 = 20 + 0.5x + 0.15 (20) + 0.15 (0.5x)

62.10 = 20 + 0.5x + 3 + 0.075x

Adding the like terms:

62.10 = (0.5x + 0.075x) + (20 + 3)

62.10 = 0.575x + 23

subtracting 23 from both sides:

we get,

39.10 = 0.575x

dividing both sides by 0.575

x = 68

As x represents the number of pages, so the maximum number of pages she can have in her book is 68.

P = $62.10

62.10 = 20 + 0.5 x + 3 + 0.075 x

0.575 x = 39.1

x = 39.1 : 0.575 = 68

Answer: The maximum number of pages is 68.