Homework 3.4 An Introduction to Problem Solving (Previo
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Question 4
A 57 -foot length of wire is to be cut into 2 pieces, so that the longer piece is 5 feet long times the shorter piece. Find the length of each piece.
Shorter Piece is feet
Longer Piece is feet
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Answer
Final Answer: The length of the shorter piece is \(\boxed{\frac{19}{2}}\) feet and the length of the longer piece is \(\boxed{\frac{95}{2}}\) feet.
Step 1 ：Let's denote the length of the shorter piece as x. Then the length of the longer piece would be 5x.
Step 2 ：The sum of these two lengths should be equal to the total length of the wire, which is 57 feet. So we have the equation: \(x + 5x = 57\)
Step 3 ：Solving this equation gives us the value of x, which represents the length of the shorter piece.
Step 4 ：Substituting x into the equation gives us the length of the longer piece as \(5x\).
Step 5 ：Final Answer: The length of the shorter piece is \(\boxed{\frac{19}{2}}\) feet and the length of the longer piece is \(\boxed{\frac{95}{2}}\) feet.
