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

Question

The equation 46 = 2 x + 2 y gives the perimeter of a rectangular rug that has length x , in feet, and width y , in feet. The width of the rug is 8 feet. What is the length, in feet, of the rug?

Accepted Answer

The correct answer is 15 . It's given that the equation 46 = 2 x + 2 y 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 = 2 x + 2 y yields 46 = 2 x + 2 8 , or 46 = 2 x + 16 . Subtracting 16 from both sides of this equation yields 30 = 2 x . 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.

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