A book designer decided that the pages of a book should have 1-in. margins at the top and bottom and
1
2
in. margins on the sides. She further stipulated that each page should have an area of 52 in.2. Find a function in the variable x, giving the area of the printed region
printed width = x
page width = x+1
page height = 52/(x+1)
printed height = 52/(x+1) - 2
printed area is x(52/(x+1) - 2) = 52x/(x+1) - 2x
To find a function in the variable x that gives the area of the printed region, let's break down the information provided.
1. The pages of the book have 1-in. margins at the top and bottom. This means that the actual printed region on each page will have a height of x - 2 inches.
- The margin at the top and bottom adds up to 1 + 1 = 2 inches, which is subtracted from the total height.
2. The pages have 1/2 in. margins on the sides. This means that the actual printed region on each page will have a width of x - 1 inch.
- The margin on each side adds up to 1/2 + 1/2 = 1 inch, which is subtracted from the total width.
3. The book designer stipulated that each page should have an area of 52 in^2.
Based on the above information, we can construct a function in the variable x to represent the area of the printed region.
Area of the printed region = (height) * (width)
Area = (x - 2) * (x - 1)
Therefore, the function in the variable x, giving the area of the printed region, is:
A(x) = (x - 2)(x - 1)