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

expand the parentheses and combine like terms

Answer 2

i got the answer thank you

Answer 3

what was the answer?

Answer 4

@MyChem

1. "expand the parentheses", or get rid of them, which is done by multiplying the terms inside of it with the number it is multiplied with:

P = (20 + 0.5x) + 0.15*(20 + 0.5x)
becomes
P = 20 + 0.5x +0.15*20 + 0.15*0.5x
= 20 + 0.5 x + 3.00 + 0.075 x.

2. "combine like terms" - we pair each type of term; in this equation, there are two "types" - those that are x terms and those that are not. we can add the values of x-terms together, and we can also add the values of non-x-terms together:

P = 23 + 0.575 x.

3. We adjust this general photobook-cost formula to the problem. Since Jennifer has $62.10 to spend, we can set "P", which is the total cost, to that pricepoint:

$62.10 = 23 + 0.575 x

now, we "just" need to solve for x in this equation, and we will know the number of pages that she can get. to do it, we could multiply both sides by 1,000 (so that x doesn't have any fractions left over):

62,100 = 23,000 + 575 x then, subtract 23,00 and divide by 575:
39,100 = 575 x
x =

...and that will be the number of pages that she can get for $62.10.