Problem

A 20 -foot piece of string is cut into two pieces so that the longer piece is 5 feet longer than twice the shorter piece. Find the lengths of both pieces. What is the length of the shorter piece?

Solution

Step 1 :Let's denote the length of the shorter piece as \(x\). According to the problem, the longer piece is 5 feet longer than twice the shorter piece, so it can be represented as \(2x + 5\). The total length of the string is 20 feet, so we can set up the equation \(x + 2x + 5 = 20\) to find the value of \(x\).

Step 2 :Solving the equation gives the length of the shorter piece of string as \(x = 5\) feet.

Step 3 :Now, we will calculate the length of the longer piece using the relationship given in the problem. The longer piece is \(2x + 5\) feet long.

Step 4 :Substituting \(x = 5\) into the equation gives the length of the longer piece as \(15\) feet.

Step 5 :Final Answer: The length of the shorter piece is \(\boxed{5}\) feet and the length of the longer piece is \(\boxed{15}\) feet.

From Solvely APP
Source: https://solvelyapp.com/problems/46056/

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