Algebra Word Problem

Question

A picture is to be put on a poster board that is 18 in. by 22 in. If there is to be an even amount of poster board around the picture, how wide should the border be if the area of the picture is 192 in ^2?

Answer 1

picture is 192 in^2

poster board is 18 by 22 inches= 18(22)=396 in^2

396-192=204 in^2 = area of the border around the picture

(18-2x)(22-2x)=192 where x = the border area width

(9-x)(11-x)= 48

99-20x+x^2 =48

x^2-20x+51=0

(x-3)(x-17)=0

x=3 inch border