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 18%. The price of a book can be modeled by the equation below, where P = the price of the book, 50 is the printing charge, 0.4 is the charge per page, and x = the number of pages:

P = (50 + 0.4x) + 0.18(50 + 0.4x)
Chris wants to purchase a book but only has $75 to spend. What is the maximum number of pages she can have in her book?
x = pages

Answer 1

To find the cost of a textbook with 400 pages, substitute x = 400 into the equation. The cost would be $247.80. For a textbook with 600 pages, substitute x = 600 into the equation. The cost would be $342.20. To obtain the graph of the regression line, use a graphing calculator or software.

Step-by-step explanation:

To find the cost of a textbook with 400 pages, we can substitute the value of x into the equation. For x = 400, the equation becomes:

P = (50 + 0.4 * 400) + 0.18(50 + 0.4 * 400)

P = (50 + 160) + 0.18(50 + 160)

P = 210 + 0.18 * 210

P = 210 + 37.8 = 247.8

Therefore, the cost of a textbook with 400 pages would be $247.80.

Similarly, for a textbook with 600 pages, we can substitute x = 600 into the equation:

P = (50 + 0.4 * 600) + 0.18(50 + 0.4 * 600)

P = (50 + 240) + 0.18(50 + 240)

P = 290 + 0.18 * 290

P = 290 + 52.2 = 342.2

Therefore, the cost of a textbook with 600 pages would be $342.20.

To obtain the graph of the regression line, you can use a graphing calculator or computer software that can plot the equation and provide a visual representation of the relationship between the number of pages and the cost of the book.