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Answer :
Final answer:
The width of the twin blanket is 126 inches and the length is 150 inches. The width of the double blanket is 126 inches and the length is 140 inches.
Explanation:
To find the dimensions of the twin blanket, let's assume its width is x inches. According to the problem, the length of the twin blanket is 24 inches longer than the width. So the length of the twin blanket is (x + 24) inches. The area of the twin blanket is given by the product of its dimensions, so the area of the twin blanket is x(x + 24) square inches
Similarly, the width of the double blanket is also x inches. But the length of the double blanket is 14 inches wider, so the length of the double blanket is (x + 14) inches. The area of the double blanket is x(x + 14) square inches.
According to the problem, the area of the twin blanket is 1,260 square inches less than the area of the double blanket. So we can set up the following equation:
x(x + 24) = x(x + 14) + 1,260
Expanding and simplifying the equation, we get:
x^2 + 24x = x^2 + 14x + 1,260
Subtracting x^2 from both sides, we get:
24x = 14x + 1,260
Subtracting 14x from both sides, we get:
10x = 1,260
Dividing both sides by 10, we get:
x = 126
So the width of the twin blanket is 126 inches. And the length of the twin blanket is (126 + 24) = 150 inches.
The dimensions of the twin blanket are therefore 126 inches by 150 inches.
To find the dimensions of the double blanket, we use the same width, which is x = 126 inches. The length of the double blanket is (126 + 14) = 140 inches.
The dimensions of the double blanket are therefore 126 inches by 140 inches.
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