The equation 46 = 2 x + 2 y gives the perimeter of a rectangular rug

The correct answer is $15$. It's given that the equation $46=2x+2y$ gives the perimeter of a rectangular rug that has length $x$, in feet, and width $y$, in feet. It's also given that the width of the rug is $8$ feet. Substituting $8$ for $y$ in the equation $46=2x+2y$ yields $46=2x+2\left(8\right)$, or $46=2x+16$. Subtracting $16$ from both sides of this equation yields $30=2x$. Dividing both sides of this equation by $2$ yields $15=x$. Since $x$ represents the length, in feet, of the rug, it follows that the length of the rug is $15$ feet.