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A 20 foot rope is cut so that one piece is 5 feet longer than the other. Let x represent the shorter piece and y represent the longer piece of rope.

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Final answer:

To find the lengths of the two pieces of rope, set up an equation and solve for x. The shorter piece is 7.5 feet long and the longer piece is 12.5 feet long.

Step-by-step explanation:

To solve this problem, we need to set up an equation based on the given information. Let x represent the length of the shorter piece of rope. Then, the length of the longer piece of rope can be represented as x+5. We know that the total length of the rope is 20 feet, so we can set up the equation x + (x+5) = 20 to solve for x.

Combining like terms, we get 2x + 5 = 20. Subtracting 5 from both sides gives 2x = 15. Finally, dividing both sides by 2 gives x = 7.5.

Therefore, the shorter piece of rope is 7.5 feet long and the longer piece of rope is 7.5 + 5 = 12.5 feet long.

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