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 piece
What is the length of the shorter piece?
5 feet
What is the length of the longer piece?
Answer
Final Answer: The length of the shorter piece is \(\boxed{5}\) feet and the length of the longer piece is \(\boxed{15}\) feet.
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 ：The solution to the equation is \(x = 5\), which means the length of the shorter piece is 5 feet.
Step 3 ：Now, we can substitute \(x = 5\) into the expression for the longer piece to find its length.
Step 4 ：Final Answer: The length of the shorter piece is \(\boxed{5}\) feet and the length of the longer piece is \(\boxed{15}\) feet.
