the printed matter on a 18 by 22 centimeter page of a book must cover 96 square centimeters.If all margins are to be the same width, how wide should they be?
Let x = margin width.
(18 - 2x)(22 - 2x) = 96
396 - 80x +4x^2 = 96
300 -80x +4x^2 = 0
x^2 -20x + 75 = 0
(x-15)(x-5) = 0
x = 5 cm is the only margin width that results in positive length and width of the printed area.
To find out the width of the margins, we first need to calculate the total area of the page. The page is given as 18 by 22 centimeters, so the total area is obtained by multiplying the length and width:
Total area = 18 cm * 22 cm
Next, we need to subtract the area that needs to be covered with printed matter from the total area to find out the remaining area for the margins:
Remaining area = Total area - 96 cm²
Now, we can calculate the width of the margins. Since all margins are of the same width, we can divide the remaining area by 4 (as there are 4 margins - top, bottom, left, and right) to get the width of each margin:
Width of each margin = Remaining area / 4
By following this calculation, we can solve for the width of the margins.