The perimeter of a rectangle is given by the formula,
[tex]P=2l+2w[/tex]
We substitute,
[tex]P=15x+17y[/tex]
and
[tex]l=\frac{7}{2}x+7y[/tex]
into the above formula to obtain the expression,
[tex]15x+17y=2(\frac{7}{2}x+7y)+2w[/tex]
[tex]15x+17y=7x+14y+2w[/tex]
We now group the x and y terms on the Left Hand Side of the equation to get.
[tex]15x-7x+17y-14y=2w[/tex]
[tex]8x+7y=2w[/tex]
We now divide through by 2 to get,
[tex]4x+\frac{7}{2}y=w[/tex]
Therefore the width of the rectangle is
[tex]4x+\frac{7}{2}y[/tex]
