A company offers blankets in two sizes: twin and double. The twin blanket is 24 inches longer than it is wide. The double blanket has the same length as the twin blanket but is 14 inches wider. The area of the twin blanket is 1,260 square inches less than the area of the double blanket.

Write an equation that can be used to determine the area of the double blanket.

To find the area of the double blanket, we define the width of the twin blanket as w inches and its length as w + 24 inches. With this, the double blanket's width is w + 14 inches. The resulting equation to determine the area of the double is (w + 14)(w + 24) = w(w + 24) + 1,260.

Explanation:

To write an equation that can be used to determine the area of the double blanket, we first need to establish variables for the width and length of the twin blanket. Let the width be w inches and the length be w + 24 inches, as the twin blanket is 24 inches longer than it is wide. The double blanket is 14 inches wider than the twin, so its width is w + 14 inches and the length remains the same as the twin, which is w + 24 inches.

The area of the twin blanket is w(w + 24), and the area of the double blanket is (w + 14)(w + 24). According to the problem, the area of the double blanket is 1,260 square inches more than the area of the twin blanket, leading to the equation:

(w + 14)(w + 24) = w(w + 24) + 1,260

Expanding and simplifying this equation will allow us to find the area of the double blanket.