Question

a 15 - foot piece of string is cut into two pieces so that the longer piece is 3 feet longer than twice the shorter piece. find the lengths of both pieces. what is the length of the shorter piece? feet what is the length of the longer piece?

Explanation:

Step1: Define variables

Let the length of the shorter piece be \( x \) feet. Then the length of the longer piece is \( 2x + 3 \) feet.

Step2: Set up equation

The total length of the string is 15 feet, so \( x+(2x + 3)=15 \).

Step3: Solve for \( x \)

Combine like terms: \( 3x+3 = 15 \). Subtract 3 from both sides: \( 3x=15 - 3=12 \). Divide by 3: \( x=\frac{12}{3}=4 \).

Step4: Find longer piece length

Substitute \( x = 4 \) into \( 2x + 3 \): \( 2(4)+3=8 + 3 = 11 \).

Answer:

Shorter piece: 4 feet
Longer piece: 11 feet