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 it is 14 inches wider. The area of the twin blanket is 1,260 square inches less than the area of the double.

Part A

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

The area of the double blanket can be represented by an equation using the width of the twin blanket as the main variable 'w'. The equation based on the given problem is (w + 14) * (w + 24) = w(w + 24) + 1260. The width w can be solved for and then used to calculate the areas of both blankets.

Explanation:

The question relates to creating an equation for the area of a double blanket, based on the given characteristics of twin and double blankets. Let's denote the width of the twin blanket as w inches.

According to the problem, the length of the twin blanket is w + 24 inches.

Since the double blanket has the same length as the twin blanket, but it is 14 inches wider, it will have a width of w + 14 inches and the same length of w + 24 inches.

The area of the twin blanket is given by w times (w + 24), and the area of the double blanket is (w + 14) times (w + 24). The problem states that the area of the double blanket is 1,260 square inches more than the area of the twin blanket. Therefore, the equation to determine the area of the double is:

(w + 14) * (w + 24) = w(w + 24) + 1260

This equation can be simplified and solved for w to find the width of the blankets and, subsequently, the area of each.