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.

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?

Answer 1

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.

Answer 2

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.