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?

x = ______________________ pages

Answer 1

The maximum number of pages she can have in her book is 68 pages

Explanation:

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.

we will put P = 62.10

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

Solving this;

`62.10 =20+0.5x+3+0.075x`

=>
`62.10 =23+0.575x`

=>
`62.10-23=0.575x`

=>
`39.1=0.575x`

x = 68

Hence, the maximum number of pages she can have in her book is 68 pages.

Answer 2

You can just substitute $62.10 to the model of the price

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

68.10 = (20 +0.5x) + 0.15(20+0.5x)

x = 68 pages

therefore the maximum number of pages she can have in her book is 68 pages