Final answer:
The lengths of both carpet rolls can be found by setting up the equation 9L = 15(L - 30) and solving for L, representing the length of the 9 feet wide carpet.
Step-by-step explanation:
The problem is a classic algebraic word problem that involves setting up an equation to find the dimensions of two rolls of carpet with the same area but different widths and lengths. Since the problem states that both rolls have the same area, we can use the formula Area = width × length to set up our equation.
Let L be the length of the 9 feet wide roll of carpet. Since the roll of carpet that is 15 feet wide is 30 feet shorter, its length would be L - 30 feet. We can set up the equation as:
9 feet × L = 15 feet × (L - 30 feet)
By solving this equation, we find the value of L which is the length of the 9 feet wide roll of carpet.