SOLUTION: I need help in solving the following. Thank you. A rectangular garden has dimensions of 23ft by 11ft. A gravel path of equal width is to be built around the garden. How wide

Question 143297: I need help in solving the following. Thank you.
A rectangular garden has dimensions of 23ft by 11ft. A gravel path of equal width is to be built around the garden. How wide can the path be if there is enough gravel for 240 square feet. I was trying to solve this by using the formula (23-2x)(11-2x) = 240 but I cant find the solution to work. Any help would be appreciated to point me in the right direction. Thank you.
Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
23*11=253^ft is the area of the garden
(23+2x)(11+2x)=253+240
253+22x+46x+4x^2=493
4x^2+68x+253-493=0
4x^2+68x-240=0
4(x^2+17x-60)=0
4(x-3)(x+20)=0
x-3=0
x=3 ft. for the width of the path.
proof:
(23+2*3)(11+2*3)=493
(23+6)(11+6)=493
29*17=493
493=493
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