SOLUTION: Solve the problem, if possible. Round your answer to the nearest tenth, when appropriate. A book has pages that are 16 cm by 20 cm. The printed matter on a page of the book mu

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Question 48559: Solve the problem, if possible. Round your answer to the nearest tenth, when appropriate.
A book has pages that are 16 cm by 20 cm. The printed matter on a page of the book must cover 140cm%5E2. If all margins are to be the same width, how wide should the margins be?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let the width of the margin be x cm.
The area of the printed matter can be represented by the length of the page less twice the margin (20-2x) times the width of the page less twice the margin (16-2x), and this is given as 140 sq.cm. You can write the appropriate equation for this:
%2820-2x%29%2816-2x%29+=+140 Perform the indicated multiplication and simplify.
320-72x%2B4x%5E2+=+140 Rewrite as:
4x%5E2-72x%2B320+=+140 Subtract 140 from both sides of the equation.
4x%5E2-72x%2B180+=+0 Factor out a 4 to simplify.
4%28x%5E2-18x%2B45%29+=+0 Apply the zero product principle.
x%5E2-18x%2B45+=+0 Solve by factoring.
%28x-3%29%28x-15%29+=+0 Apply the zero product principle.
x-3+=+0 and/or x-15+=+0
If x-3+=+0 then x+=+3
If x-15+=+0 then x+=+15
The margin is either 3 cm wide or 15 cm wide.
But if the margin were 15 cm wide, there would be no space for the printed matter because the page is only 16 cm wide and the margin of 15 cm on both sides of the page just doesn't make any practical sense...so discard the 15 cm solution.
The margin has to be 3 cm wide.