You are putting a stone border along two sides of a rectangular Japanese garden that measures [b][i]6[/i][/b] yards by [b][i]15[/i][/b] yards. Your budget limits you to only enough stones to cover [b][i]46[/i][/b] square yards. How wide should the border be?

Begin by drawing and labeling a diagram.[br][br]Area of Border = Total Area - Garden Area[br][br][math]46=\left(x+15\right)\left(x+6\right)-\left(15\right)\left(6\right)[/math]    [color=#1155cc]Write quadratic model.[/color][br][br][math]46=x^2+21x+90-90[/math]      [color=#1155cc]Multiply[/color][br][br][math]0=x^2+21x-46[/math]       [color=#1155cc]Write in standard form[/color][br][br][math]0=\left(x+23\right)\left(x-2\right)[/math]        [color=#1155cc]Factor[/color][br][br][math]\left(x+23\right)=0[/math] or [math]\left(x-2\right)=0[/math]   [color=#1155cc]Use zero-product property[/color][br][br][math]x+23=0[/math]          [color=#1155cc]Set first factor equal to 0[/color][br][br][math]x=-23[/math]          [color=#1155cc]Solve for x[/color][br][br][math]x-2=0[/math][color=#1155cc]      Set second factor equal to 0[/color][br][br][math]x=2[/math][color=#1155cc]       Solve for x[/color][br][br]The solutions are [math]-23[/math] and [math]2[/math]. Only [math]x=2[/math] is a reasonable solution, because negative values for dimensions do not make sense. Mark the border [color=#ff0000]2 yards[/color] wide.